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Development of a Quantitative Safety Risk Assessment Model for Rail Safety Management System Its Application towards Assessing and Prioritising Safety Risks at Interfaces of Railway and Highway by RAJALINGAM RAJAYOGAN M.Sc., University of South Bank, London (1994) B.Eng. (Mech), University of Peradeniya, Sri Lanka (1982) A Thesis Submitted in Partial Fulfilment of the Requirements for the Degree of Doctor of Philosophy School of Business University of Western Sydney Australia February 2012
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Page 1: Development of a Quantitative Safety Risk Assessment Model ...€¦ · Development of a Quantitative Safety Risk Assessment Model for Rail Safety Management System Its Application

Development of a Quantitative Safety Risk Assessment Model for Rail Safety Management System

Its Application towards Assessing and Prioritising Safety Risks

at Interfaces of Railway and Highway

by

RAJALINGAM RAJAYOGAN M.Sc., University of South Bank, London (1994)

B.Eng. (Mech), University of Peradeniya, Sri Lanka (1982)

A Thesis Submitted in Partial Fulfilment of the Requirements for the Degree of

Doctor of Philosophy

School of Business University of Western Sydney

Australia

February 2012

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Dedication

I dedicate this thesis to my almighty God ‘Lord Ganesha’ and to

my beloved Bhagawan ‘Sri Sathiya Sai Baba’, who gave me love and huge blessings

to initiate and to successfully complete my doctoral studies.

(Aum Ganeshaya Namaha & Aum Sai Ram)

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Declaration of Originality

This is to certify that the research work reported in this thesis is, to the best of my

knowledge and belief, original and has not been submitted to any other University or

Institution for the award of a higher degree.

Rajalingam Rajayogan

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Acknowledgment

During my doctoral studies at the University of Western Sydney, I have had a great

opportunity to work on my favourite topic which is directly related to the nature of

my current employment at RailCorp-NSW. Through this study I have gained very

interesting and valuable experiences while meeting many local and international

people, colleagues and friends who helped me with my research along the way, either

directly or indirectly. I therefore take this opportunity to express my sincere

appreciation and gratitude to them.

First and foremost, I am deeply grateful to my principal supervisor Dr Premaratne

Samaranayake for his gentle encouragement and guidance, and my co-supervisor

Dr Kenan Matawie for his assistance in the statistical analysis of this study. I would

like to thank my former supervisors Dr K Ramanathan, Dr V Jayaraman and

Dr R Agrawal. I also thank my friends Dr P Jayakumar and Dr D Jeyaraman who

initiated the wonderful idea about PhD studies in my mind.

I express my sincere thanks to Dr Siriyani Dias, Ms Maria Lozano and Mr Tony

Davies from my previous employment at WorkCover-NSW, who assisted me in

learning the statistical analysis system in order to conduct statistical research work. I

also thank Mr Ian Cooke for helping me in the initial preparation of data. It is also

necessary to thank my current employer (RailCorp-NSW) and my work supervisors

Mr Matthew Coates and Ms Mandie Thomas for allowing me to take considerable

time off from my work to undertake this study at the University.

I offer my sincere salutes to my beloved leader late Dr M G Ramachandran (MGR)

who gave me courage and self confidence indirectly. My sincere appreciations go to

Prof. E. Ambikairajah and my family friends (including the members of our music

group ‘Sydney Geetha Saagara’) who provided assistance in various ways.

Finally, I would like to especially thank my wife Naguleswary (Rahini), my daughter

Sujanthini and my son Shayanthan who offered me love, patience and moral support

during my studies.

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Table of Contents

PAGE

Dedication ............................................................................................................................................. ii

Declaration of Origina lity................................................................................................................... iii

Acknowledgement ............................................................................................................................... iv

Table of Contents ................................................................................................................................. v

List of Tables ........................................................................................................................................ x

List of Figures.................................................................................................................................... xiii

Abbreviations ..................................................................................................................................... xv

Nomenclature .................................................................................................................................... xvi

Abstract............................................................................................................................................. xvii

Chapter 1: Introduction to the Research...............................................................................................................1

1.0 Introduction .................................................................................................................................1 1.1 Overview of Risk and Occupational Health & Safety.................................................................1 1.2 Safety Management System (SMS).............................................................................................4 1.3 Background of Rail Safety Risk Potentials and Rail SMS ..........................................................5 1.4 Significance of the Study.............................................................................................................8 1.5 Objectives of the Study .............................................................................................................10 1.6 Target of the Study ....................................................................................................................11 1.7 Benefits of the Study .................................................................................................................12 1.8 Limitations of the Study ............................................................................................................13 1.9 Structure of the Thesis...............................................................................................................14

Chapter 2: Literature Review...............................................................................................................................18

2.0 Introduction ...............................................................................................................................18 2.1 Definitions of Terms Used in Relations to Safety .....................................................................18

2.1.1 Accidents ...........................................................................................................................19 2.1.2 Hazards ..............................................................................................................................20 2.1.3 Risks ..................................................................................................................................21 2.1.4 Safety.................................................................................................................................23

2.2 Safety Management System (SMS) at Organisational Level ....................................................24 2.2.1 The Four ‘P’ Principles of Safety Management System....................................................25 2.2.2 Safety Culture ....................................................................................................................27 2.2.3 Organisational Involvement in SMS..................................................................................28 2.2.4 Comparison of Current SMS with Traditional Approach ..................................................29 2.2.5 Major Modules of SMS .....................................................................................................30 2.2.6 Initiatives to Build an SMS................................................................................................ 31

2.2.6.1 Employer’s Responsibilities ......................................................................................31 2.2.6.2 Leadership Skills........................................................................................................ 32 2.2.6.3 Communicating Safety Critical Information..............................................................33 2.2.6.4 Elements of a Safe Working Environment.................................................................34

2.2.7 Measurements on Effectiveness of SMS ...........................................................................37 2.3 Risk Management within SMS.................................................................................................. 38

2.3.1 Major Processes in Risk Management...............................................................................39 2.3.2 Hazard Identification .........................................................................................................40

2.3.2.1 Dividing Hazard Identification into Manageable Portions.........................................40 2.3.2.2 Developing an Inventory of Tasks .............................................................................41 2.3.2.3 Analysing Tasks......................................................................................................... 41

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2.3.2.4 Identifying the Hazards Involved...............................................................................42 2.3.2.5 Considering the People Factor ...................................................................................42 2.3.2.6 Aiding Hazard Identification .....................................................................................43 2.3.2.7 Hazard Identification as Ongoing Process .................................................................45 2.3.2.8 Recording Hazard Identification Data........................................................................45

2.3.3 Undertaking Risk Assessment ...........................................................................................46 2.3.3.1 Risk Assessment ........................................................................................................46 2.3.3.2 Risk Assessment Matrix.............................................................................................48 2.3.3.3 Recording Results of Risk Assessment......................................................................51 2.3.3.4 Considering Current Controls ....................................................................................52 2.3.3.5 Setting Times Limits for Action ................................................................................52

2.3.4 Risk Control or Elimination............................................................................................... 53 2.3.4.1 Risk Control Involvement..........................................................................................53 2.3.4.2 Hierarchy of Controls ................................................................................................54 2.3.4.3 Sequence of Risk Control ..........................................................................................55 2.3.4.4 Undertaking Monitoring and Review.........................................................................57

2.4 Safety Risk Potentials in Railways............................................................................................ 58 2.4.1 Priority Issues Identified in Rail Safety .............................................................................60

2.4.1.1 System Based Safety Issues .......................................................................................61 2.4.1.2 People Based Safety Issues ........................................................................................64

2.4.2 Challenges of Safety Faced in Rail Sector.........................................................................68 2.5 Rail Safety Management System............................................................................................... 70

2.5.1 Rail SMS as a Central System to All Rail Operations.......................................................71 2.5.2 Development and Management of Rail Safety ..................................................................74 2.5.3 Key Components of SMS Managed by Rail Sectors .........................................................74 2.5.4 External Bodies Assisting in Rail Safety ...........................................................................79 2.5.5 Need for Measuring Rail Safety ........................................................................................81 2.5.6 Risk Assessment in Rail SMS ...........................................................................................82

2.6 Major Safety Issues at Railway-Highway Interfaces.................................................................84 2.6.1 Statistical Overview of Global Level Crossing Collisions and Consequences ..................85 2.6.2 Global Comparison of Level Crossing Accidents..............................................................87

2.6.2.1 Level Crossing Collisions ..........................................................................................87 2.6.2.2 Level Crossing Fatalities............................................................................................88

2.7 Background of Research Problem .............................................................................................89 2.7.1 Significance of Safety Improvement at Level Crossings...................................................90

2.7.2 Previous Research on Risk Assessment at Grade Crossings.........................................90 2.7.3 The Need for Improving Railway Grade Crossings Safety ...............................................91

2.8 Summary ...................................................................................................................................93 Chapter 3: Research Methodology.......................................................................................................................94

3.0 Introduction ...............................................................................................................................94 3.1 Fundamental Concepts on Safety Risks Evaluation ..................................................................94

3.1.1 Identification of General Risks ..........................................................................................95 3.1.2 Evaluation of Risks............................................................................................................96 3.1.3 Analysis of Risk.................................................................................................................97 3.1.4 Types of Risk Analysis Methods .......................................................................................98

3.1.4.1 Qualitative Risk Analysis...........................................................................................99 3.1.4.2 Quantitative Risk Analysis.......................................................................................101 3.1.4.3 Semi-Quantitative Risk Analysis .............................................................................103

3.2 Developing Theoretical Framework on Safety Risk Evaluation at Rail Grade Crossings.......103 3.2.1 Development of a Quantitative Risk Assessment Model for Safety Evaluation at Rail Crossings - Safety Risk Index (SRI).........................................................................................104

3.2.1.1 Basic Concepts Used in Developing SRI.................................................................105 3.2.1.2 Numerical Example on Application of SRI .............................................................107 3.2.1.3 Major Steps to Achieve Objectives of Study ...........................................................108 3.2.1.4 Grade Crossing Accidents Data for Analysis...........................................................110

3.2.2 Major Factors Influencing Accident Risks at Grade Crossings .......................................111 3.2.2.1 Crossings Characteristics .........................................................................................113 3.2.2.2 Railway Characteristics............................................................................................114

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3.2.2.3 Highway Characteristics ..........................................................................................114 3.2.2.4 Vehicle Attributes ....................................................................................................115 3.2.2.5 Driver Attributes ......................................................................................................115 3.2.2.6 Environmental Attributes.........................................................................................115

3.3 Overview of Current Statistical Models for Predicting Accidents and Consequences at Grade Crossings .......................................................................................................................................116

3.3.1 Review on Common Models Predicting Highway Accidents..........................................117 3.3.1.1 Poisson Regression Models .....................................................................................119 3.3.1.2 Negative Binomial Regression Models....................................................................120 3.3.1.3 Gamma Models........................................................................................................120 3.3.1.4 Zero-Inflated Poisson Models..................................................................................121 3.3.1.5 Empirical Bayesian Model.......................................................................................123

3.3.2 Overview on Existing Models Developed for Prediction of Collisions at Railway-Highway Interfaces ..................................................................................................................................123

3.3.2.1 Relative Risk Models...............................................................................................125 3.3.2.2 Absolute Risk Models..............................................................................................127

3.3.3 Overview of Existing Models in Predicting Consequences of Collisions at Railway-Highway Interfaces...................................................................................................................131

3.3.3.1 USDOT Consequence Model (1987).......................................................................132 3.3.3.2 Canada - University of Waterloo Consequence Model (2003) ................................133

3.3.4 Overview of Existing Models in Predicting Overall Safety Risks at Railway-Highway Interfaces ..................................................................................................................................134

3.4 Evaluation of Risk at Grade Crossings with Application of Safety Risk Index (SRI).............134 3.4.1 Identifying Worst Accident Crossing Locations (Black-Spots).......................................135 3.4.2 Developing an Improved Quantitative Method for Black-Spots Identification with Application of SRI....................................................................................................................136

3.5 Summary .................................................................................................................................138 Chapter 4: Data Collection and Consolidation ................................................................................................. 140

4.0 Introduction .............................................................................................................................140 4.1 Source of Rail Crossing Accidents Data and Information.......................................................140

4.1.1 Database of Railway-Highway Crossings Data and Information (Inventory Database)..141 4.1.1.1 Attributes and Variables in Inventory Database.......................................................142 4.1.1.2 Selection of Appropriate Variables from Inventory Database .................................143 4.1.1.3 Extraction of Public Grade Crossings from Inventory Database .............................146

4.1.2 Database of Railway-Highway Crossing Accidents Information (Occurrence Database)149 4.1.2.1 Attributes and Variables in Occurrence Database....................................................149 4.1.2.2 Selection of Appropriate Variables for Developing Models....................................150 4.1.2.3 Selection of Appropriate Records from Occurrence Database.................................152

4.1.3 Consolidated Database by Combining Inventory and Occurrence Databases .................154 4.2 Preliminary Data Analysis on Rail Crossings Accidents.........................................................155

4.2.1 Accidents at All Railway-Highway Crossings.................................................................156 4.2.1.1 Annual Accident Rates for All Rail Crossings Relations to Travel .........................157 4.2.1.2 Annual Accident Frequency Rates for Rail Crossings.............................................159 4.2.1.3 Reasons for Research Focus on Public Grade Crossings .........................................160

4.2.2 Accidents and Consequences at Public Grade Crossings ................................................163 4.2.2.1 Reasons for Grouping Public Grade Crossings by Protection Types for Model Development........................................................................................................................164 4.2.2.2 Inventory Data on Public Grade Crossings by Protection Type...............................164 4.2.2.3 Statistics of Accident Frequency and Consequence for Public Grade Crossings by Protection Type (2001 – 2005) ............................................................................................165 4.2.2.4 Statistics of Variables Used in Models by Protection Types ...................................166

4.3 Summary .................................................................................................................................166 Chapter 5: Development and Validation of Grade Crossing Accidents and Consequences Prediction Models............................................................................................................................................................168

5.0 Introduction .............................................................................................................................168 5.1 Overview of Current Safety Risk Assessment Models............................................................169

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5.2 Common Models of Accident Frequency Prediction ..............................................................170 5.2.1 Poisson Models................................................................................................................171

5.2.1.1 Poisson Distribution.................................................................................................171 5.2.1.2 Zero-Inflated Poisson Distribution...........................................................................176 5.2.1.3 Multiplicative Poisson Regression Distribution.......................................................185

5.2.2 Negative Binomial Regression Model .............................................................................186 5.2.3 Empirical Bayesian (EB) Model......................................................................................188

5.3 Common Models of Accidental Consequences Prediction......................................................190 5.3.1 Consequence Model by US Department of Transportation .............................................191 5.3.2 Consequence Model by Canada Transport Development Centre ....................................192

5.4 Major Steps in the Process of Model Development ................................................................193 5.4.1 Functional Form of Model...............................................................................................196 5.4.2 Model Distribution Structure ...........................................................................................197

5.4.2.1 Poisson Distribution.................................................................................................197 5.4.2.2 Gamma Distribution.................................................................................................197 5.4.2.3 Negative Binomial Distribution ...............................................................................198 5.4.2.4 Empirical Bayesian ..................................................................................................199

5.4.3 Selection of Explanatory Variables for a Best-Fit Model................................................199 5.4.4 Procedures for Selecting Appropriate Variables for a Model ..........................................200 5.4.5 Assessment of Final Model for Goodness-of-Fit .............................................................201 5.4.6 Procedures for Selecting Final Model..............................................................................202

5.4.6.1 Step-1: Developing a GLM Poisson Regression Model ..........................................202 5.4.6.2 Step-2: Developing a GLM Negative Binomial Regression Model.........................202 5.4.6.3 Step-3: Selection of Appropriate Model - Poisson or Negative Binomial ...............202 5.4.6.4 Step-4: Utilising Empirical Bayesian Models..........................................................203

5.5 Results on Models Developed for Each Protection Type ........................................................208 5.5.1 Generating Models Predicting Accident Frequencies......................................................209

5.5.1.1 Crossing Protection Type 1 (No Signs or No signals) .............................................210 5.5.1.2 Crossing Protection Type 2 (Stop Signs or Cross-bucks) ........................................217 5.5.1.3 Crossing Protection Type 3 (Signals, Bells or Warning Devices) ...........................226 5.5.1.4 Crossing Protection Type 4 (Gates or Full Barrier) .................................................234

5.5.2 Generating Models Predicting Accidental Consequences ...............................................242 5.5.2.1 Crossing Protection Type 1 (No Signs or No signals) .............................................245 5.5.2.2 Crossing Protection Type 2 (Stop Signs or Cross-bucks) ........................................253 5.5.2.3 Crossing Protection Type 3 (Signals, Bells or Warning Devices) ...........................260 5.5.2.4 Crossing Protection Type 4 (Gates or Full Barrier) .................................................267

5.6 Summary .................................................................................................................................274 Chapter 6: Development of Safety Risk Index (SRI) for Risks Assessment at Grade Crossings .................276

6.0 Introduction .............................................................................................................................276 6.1 Development of Safety Risk Index (SRI) Model.....................................................................277

6.1.1 Defining Safety Risk Index (SRI)....................................................................................277 6.1.2 Identifying Safety Status of a Crossing using Graphical Method....................................278

6.2 Identifying Black-Spots (Crossings with Unacceptable Higher Safety Risk Index Values) ...280 6.2.1 Introducing Threshold Curves of Safety Risk Index........................................................280 6.2.2 Selecting Safety Risk Index Threshold Value .................................................................281 6.2.3 Identifying Black-Spots in Each Protection Type............................................................284

6.2.3.1 Crossing Protection Type 1 (No Signs or No signals) .............................................284 6.2.3.2 Crossing Protection Type 2 (Stop Signs or Cross-bucks) ........................................286 6.2.3.3 Crossing Protection Type 3 (Signals, Bells or Warning Devices) ...........................287 6.2.3.4 Crossing Protection Type 4 (Gates or Full Barrier) .................................................289

6.2.4 List of All Black-Spots Identified in the Study................................................................291 6.2.5 Validation of Safety Risk Index (SRI) Model .................................................................305 6.2.6 Analysis of Black-spot Cluster Regions (All Protection Types)......................................307

6.3 Summary .................................................................................................................................309 Chapter 7: Impact Analysis on Risk Assessment Models ................................................................................310

7.0 Introduction .............................................................................................................................310

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7.1 Impact (Sensitivity) An alysis .................................................................................................. 310 7.2 Examining Models Predicting Collisions ................................................................................312

7.2.1 Effects of Highway Characteristics on Four Protection Types........................................313 7.2.2 Effects of Railway Characteristics on Four Protection Types .........................................315 7.2.3 Effects of Upgrading Protection Types on Collisions Related to Highway Characteristics..................................................................................................................................................318 7.2.4 Effects of Upgrading Protection Types on Collisions Related to Railway Characteristics..................................................................................................................................................321

7.3 Examining Models Predicting Consequences .........................................................................324 7.3.1 Effects of Highway Characteristics on Four Protection Types........................................325 7.3.2 Effects of Railway Characteristics on Four Protection Types .........................................325

7.4 Examining Models Predicting Safety Risk Index (SRI) ..........................................................326 7.4.1 Effects of Highway Characteristics on Four Protection Types........................................327 7.4.2 Effects of Railway Characteristics on Four Protection Types .........................................331

7.5 Summary .................................................................................................................................334 Chapter 8: Conclusions and Recommendations ...............................................................................................336

8.0 Introduction .............................................................................................................................336 8.1 Overview of Research Findings ..............................................................................................337

8.1.1 Accident Frequency Prediction Model ............................................................................339 8.1.2 Accident Consequences Prediction Model ......................................................................340 8.1.3 Estimation of Safety Risk Index (SRI) ............................................................................342 8.1.4 Black-Spots Identified Using Safety Risk Index .............................................................343

8.2 Contributions of Research Study............................................................................................. 345 8.3 Benefits of Research Study ..................................................................................................... 347 8.4 Research Limitations...............................................................................................................348 8.5 Recommendations ...................................................................................................................349 8.6 Future Research.......................................................................................................................350

References .........................................................................................................................................353

Bibliogr aphy .....................................................................................................................................366

Appendix 1: All Variables in USDOT FRA Databases .................................................................369

Appendix 2: Graphical Distribution of Variables Used................................................................376

Appendix 3: Descriptive Statistics on Model Variables ................................................................386

Appendix 4: List of Publications.....................................................................................................389

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List of Tables

PAGE

Chapter 2: Table 2.1: Typical Measure of Risk Exposures 49 Table 2.2: Typical Measure of Likelihood 49 Table 2.3: Typical Measure of Consequences 50 Table 2.4: A Typical Risks Assessment Matrix 50 Table 2.5: Level Crossing Accident Statistics in Selected European Countries 87 Chapter 3: Table 3.1: Group Selection for Estimating Probability of an Event 100 Table 3.2: Group Selection for Measuring Consequences of an Event 100 Table 3.3: A Typical Qualitative Risks Ranking Matrix 101 Table 3.4: Probability of Deaths by Causes 102 Table 3.5: USDOT Accident Prediction Equations for Category by Characteristic Factors 130 Table 3.6: Coefficients of Coleman-Stewart Model 131 Chapter 4: Table 4.1: Filtering Process in Selecting Appropriate Variables from Inventory Database 146 Table 4.2: Number of All Crossings by Type Vs Position (2001-2005) 147 Table 4.3: Filtering Process in Selecting Appropriate Variables from Accident Database 152 Table 4.4: All Level Crossing Accidents and Casualties (2001 – 2005) 156 Table 4.5: Number of All Level Crossing Accidents and Accident Rates (2001 – 2005) 158 Table 4.6: Accident Frequency Rates by Type of Crossings 160 Table 4.7: Accident Frequency Rates by Type by Position of Crossings 161 Table 4.8: Public Grade Crossing Accident Casualties (2001 – 2005) 163 Table 4.9: Public Grade Crossings Data by Protection Type (2001 – 2005) 165 Table 4.10: Accidents Data of Public Grade Crossings by Protection Type (2001-2005) 165 Table 4.11: Consequences Data of Public Grade Crossings by Protection Type (2001-2005) 166 Chapter 5: Table 5.1: Comparison of Accidental Crossings Predicted by Poisson Model to History 173 Table 5.2: Over-Dispersion Test Values on Number of Accidents by Crossing Types 178 Table 5.3: Comparison of Observed and Predicted Values for Accidental Crossings by ZIP 184 Table 5.4: Descriptive Statistics on Variables Used in the Model - Protection Type 1 210 Table 5.5: Pearson Correlation Between Variables Used in the Model - Protection Type 1 211 Table 5.6: Parameter Estimates of GLM Poisson Regression Model - Protection Type 1 211 Table 5.7: Goodness-of-Fit Result of GLM Poisson Regression Model - Protection Type 1 212 Table 5.8: Parameter Estimates in GLM Negative Binomial Model - Protection Type 1 213 Table 5.9: Goodness-of-Fit Result of GLM Negative Binomial Model - Protection Type 1 213 Table 5.10: Over-Dispersion Parameter and Weighting Factors Estimation - EB Model 214 Table 5.11: Goodness-of-Fit Result of NB & EB Models - Max Timetable Train Speed 215 Table 5.12: Goodness-of-Fit Result of NB & EB Models - AADT 216 Table 5.13: Top Ten Accidental Locations by EB Model Prediction in Protection Type 1 217 Table 5.14: Descriptive Statistics on Variables Used in the Model - Protection Type 2 218 Table 5.15: Pearson Correlation Between Variables Used in the Model - Protection Type 2 218 Table 5.16: Parameter Estimates in GLM Poisson Regression Model - Protection Type 2 219 Table 5.17: Goodness-of-Fit Result of GLM Poisson Regression Model - Protection Type 2 219 Table 5.18: Parameter Estimates in GLM Negative Binomial Model - Protection Type 2 220 Table 5.19: Goodness-of-Fit Result of GLM Negative Binomial Model - Protection Type 2 220 Table 5.20: Over-Dispersion Parameter and Weighting Factors Estimation - EB Model 222 Table 5.21: Goodness-of-Fit Result of NB & EB Models - Timetable Train Speed 223 Table 5.22: Goodness-of-Fit Result of NB & EB Models - Highway Speed 223 Table 5.23: Goodness-of-Fit Result of NB & EB Models - Number of Traffic Lanes 224 Table 5.24: Goodness-of-Fit Result of NB & EB Models - Daily Train Movement 224 Table 5.25: Goodness-of-Fit Result of NB & EB Models - AADT 224 Table 5.26: Top Ten Accidental Locations by EB Model Prediction in Protection Type 2 225

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Table 5.27: Descriptive Statistics on Variables Used in the Model - Protection Type 3 226 Table 5.28: Pearson Correlation Between Variables Used in the Model - Protection Type 3 227 Table 5.29: Parameter Estimates in GLM Poisson Regression Model - Protection Type 3 227 Table 5.30: Goodness-of-Fit Result of GLM Poisson Regression Model - Protection Type 3 228 Table 5.31: Parameter Estimates in GLM Negative Binomial Model - Protection Type 3 229 Table 5.32: Goodness-of-Fit Result of GLM Negative Binomial Model - Protection Type 3 229 Table 5.33: Over-Dispersion Parameter and Weighting Factors Estimation - EB Model 230 Table 5.34: Goodness-of-Fit Result of NB & EB Models - Max Timetable Train Speed 232 Table 5.35: Goodness-of-Fit Result of NB & EB Models - Highway Speed 232 Table 5.36: Goodness-of-Fit Result of NB & EB Models - Number of Traffic Lanes 232 Table 5.37: Goodness-of-Fit Result of NB & EB Models - Daily Train Movement 233 Table 5.38: Goodness-of-Fit Result of NB & EB Models - AADT 233 Table 5.39: Top Ten Accidental Locations by EB Model Prediction in Protection Type 3 234 Table 5.40: Descriptive Statistics on Variables Used in the Model - Protection Type 4 235 Table 5.41: Pearson Correlation Between Variables Used in the Model - Protection Type 4 235 Table 5.42: Parameter Estimates in GLM Poisson Regression Model - Protection Type 4 236 Table 5.43: Goodness-of-Fit Result of GLM Poisson Regression Model - Protection Type 4 236 Table 5.44: Parameter Estimates in GLM Negative Binomial Model - Protection Type 4 237 Table 5.45: Goodness-of-Fit Result of GLM Negative Binomial Model - Protection Type 4 237 Table 5.46: Over-Dispersion Parameter and Weighting Factors Estimation - EB Model 239 Table 5.47: Goodness-of-Fit Result of NB & EB Models - Number of Main Tracks 240 Table 5.48: Goodness-of-Fit Result of NB & EB Models - Number of Traffic Lanes 240 Table 5.49: Goodness-of-Fit Result of NB & EB Models - Daily Train Movement 241 Table 5.50: Goodness-of-Fit Result of NB & EB Models - AADT 241 Table 5.51: Top Ten Accidental Locations by EB Model Prediction in Protection Type 4 242 Table 5.52: Equivalent Fatality Score comparison for various accident consequences 243 Table 5.53: Descriptive Statistics on Variables Used in the Model - Protection Type 1 245 Table 5.54: Pearson Correlation Between Variables Used in the Model - Protection Type 1 246 Table 5.55: Parameter Estimates in GLM Poisson Regression Model - Protection Type 1 246 Table 5.56: Goodness-of-Fit Result of GLM Poisson Regression Model - Protection Type 1 247 Table 5.57: Parameter Estimates in GLM Negative Binomial Model - Protection Type 1 248 Table 5.58: Goodness-of-Fit Result of GLM Negative Binomial Model - Protection Type 1 248 Table 5.59: Over-Dispersion Parameter and Weighting Factors Estimation - EB Model 249 Table 5.60: Goodness-of-Fit Result of NB & EB Models - Max Timetable Train Speed 251 Table 5.61: Goodness-of-Fit Result of NB & EB Models - Total Occupants in Vehicle 251 Table 5.62: Top Ten Locations by Consequence Predicted with EB in Protection Type 1 252 Table 5.63: Descriptive Statistics on Variables Used in the Model - Protection Type 2 253 Table 5.64: Pearson Correlation Between Variables Used in the Model - Protection Type 2 254 Table 5.65: Parameter Estimates in GLM Poisson Regression Model - Protection Type 2 254 Table 5.66: Goodness-of-Fit Result of GLM Poisson Regression Model - Protection Type 2 255 Table 5.67: Parameter Estimates in GLM Negative Binomial Model - Protection Type 2 256 Table 5.68: Goodness-of-Fit Result of GLM Negative Binomial Model - Protection Type 2 256 Table 5.69: Over-Dispersion Parameter and Weighting Factors Estimation - EB Model 257 Table 5.70: Goodness-of-Fit Result of NB & EB Models - Max Timetable Train Speed 259 Table 5.71: Goodness-of-Fit Result of NB & EB Models - Total Occupants in Vehicle 259 Table 5.72: Top Ten Locations by Consequence Predicted with EB in Protection Type 2 260 Table 5.73: Descriptive Statistics on Variables Used in the Model - Protection Type 3 261 Table 5.74: Pearson Correlation Between Variables Used in the Model - Protection Type 3 261 Table 5.75: Parameter Estimates in GLM Poisson Regression Model - Protection Type 3 262 Table 5.76: Goodness-of-Fit Result of GLM Poisson Regression Model - Protection Type 3 262 Table 5.77: Parameter Estimates in GLM Negative Binomial Model - Protection Type 3 263 Table 5.78: Goodness-of-Fit Result of GLM Negative Binomial Model - Protection Type 3 263 Table 5.79: Over-Dispersion Parameter and Weighting Factors Estimation - EB Model 264 Table 5.80: Goodness-of-Fit Result of NB & EB Models - Max Timetable Train Speed 266 Table 5.81: Goodness-of-Fit Result of NB & EB Models - Total Occupants in Vehicle 266 Table 5.82: Top Ten Locations by Consequence Predicted with EB in Protection Type 3 267 Table 5.83: Descriptive Statistics on Variables Used in the Model - Protection Type 4 268 Table 5.84: Pearson Correlation Between Variables Used in the Model - Protection Type 4 268 Table 5.85: Parameter Estimates in GLM Poisson Regression Model - Protection Type 4 269 Table 5.86: Goodness-of-Fit Result of GLM Poisson Regression Model - Protection Type 4 269

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Table 5.87: Parameter Estimates in GLM Negative Binomial Model - Protection Type 4 270 Table 5.88: Goodness-of-Fit Result of GLM Negative Binomial Model - Protection Type 4 270 Table 5.89: Over-Dispersion Parameter and Weighting Factors Estimation - EB Model 271 Table 5.90: Goodness-of-Fit Result of NB & EB Models - Max Timetable Train Speed 273 Table 5.91: Goodness-of-Fit Result of NB & EB Models - Total Occupants in Vehicle 273 Table 5.92: Top Ten Locations by Consequence Predicted with EB in Protection Type 4 273 Chapter 6: Table 6.1: Summary of Proposed Threshold Critical Values by Protection Types 283 Table 6.2: List of 3 Black-Spots Identified in Protection Type 1 286 Table 6.3: List of Top Five within 129 Black-Spots Identified in Protection Type 2 287 Table 6.4: List of Top Five within 76 Black-Spots Identified in Protection Type 3 289 Table 6.5: List of Top Five within 239 Black-Spots Identified in Protection Type 4 290 Table 6.6: List of 447 Black-Spots Identified from the Study and Their Locations 292 Table 6.7: Number of Black-Spots Identified by Top Ten States 305 Table 6.8: Number of Black-Spots Identified by Top Eight Counties 305 Table 6.9: Common 17 Black-Spots Identified in All Three Circles (A, B and C) 306 Chapter 7: Table 7.1: Controlled Values for Parameters Constructing Collision Prediction Models 312 Table 7.2: Controlled Values for Parameters Constructing Consequence Prediction Models 324 Table 7.3: Controlled Values for Parameters Constructing Safety Risk Index Models 327 Chapter 8: Table 8.1: EB Modelling Equations for Accident Frequency Prediction with Variables 339 Table 8.2: Impact Effect of Railway and Highway Characteristics on Accident Prediction 340 Table 8.3: EB Modelling Equations for Consequence Prediction with Explained Variables 341 Table 8.4: Impact Effect of All Factors on Consequences Prediction by Protection Type 342

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List of Figures

PAGE

Chapter 1: Figure 1.1: A Typical Railway-Highway Crossing in Australia 8 Figure 1.2: Outcome of a Major Accident at Level Crossing (Lismore, Australia 2006) 9 Figure 1.3: Logical Flow of Research Areas Leading to the Thesis Topic 15 Figure 1.4: Flow Diagram for Developing Structure of the Thesis 17 Chapter 2: Figure 2.1: Characteristics of an Event of Accident 19 Figure 2.2: The 4 ‘P’s Principles for Safety Management System 26 Figure 2.3: The Basic Safety Management System Process 29 Figure 2.4: The 3 ‘C’ Elements of Leadership 33 Figure 2.5: Three Major Processes in Risk Management System 39 Figure 2.6: Three Elements in Determination of Risk Assessment 47 Figure 2.7: Two Major Groups Identified in Rail Safety Issues 60 Figure 2.8: Rail Safety Management System as a Central System to All Rail Operations 73 Figure 2.9: International Comparison of Annual Collision Rate for Level Crossings 88 Figure 2.10: International Comparison of Annual Fatality Rate for Level Crossings 88 Chapter 3: Figure 3.1: Three Common Types in Risk Analysis Methods 99 Figure 3.2: Three Basic Elements of Measurements in the Development of SRI 106 Figure 3.3: Graphical Representation of Three Elements of Rail Safety Risk Evaluation 107 Figure 3.4: Flow Diagram for Identifying Black-Spots Within Grade Crossings 110 Figure 3.5: Model of Accident Risk Factors and Associated Variables at Grade Crossings 112 Figure 3.6: Graphical Model of a Typical Quantitative Safety Risk Matrix 135 Figure 3.7: Flow Diagram for Procedures of Identifying Black-Spots 136 Figure 3.8: Identifying Black-Spots within Grade Crossings Based on Safety Risk Index 137 Chapter 4: Figure 4.1: Distribution of Different Categories of Variables in the Inventory Database 142 Figure 4.2: Process for Extraction of Public Grade Crossings from Inventory Database 148 Figure 4.3: Distribution of Different Categories of Variables in the Occurrence Database 150 Figure 4.4: Process for Extraction of Crossings Accidents Information 153 Figure 4.5: All Level Crossing Accidents and Casualties (2001 – 2005) 157 Figure 4.6: Number of All Level Crossing Accidents and Accident Rates (2001 – 2005) 158 Figure 4.7: Number of Level Crossing Accidents by Crossing Type (2001 – 2005) 159 Figure 4.8: Annual Accident Frequency Rate per Crossing Type 160 Figure 4.9: Number of Crossings within Each Type of Crossing (2001 – 2005) 161 Figure 4.10: Number of Accidents within Each Type of Crossing (2001 – 2005) 162 Figure 4.11: Accident Frequency Rates within Each Type of Crossing (2001 – 2005) 162 Figure 4.12: Public Grade Crossing Accidents and Casualties (2001 – 2005) 163 Chapter 5: Figure 5.1: Number of Crossings Predicted by Poisson Model for Protection Type 1 174 Figure 5.2: Number of Crossings Predicted by Poisson Model for Protection Type 2 174 Figure 5.3: Number of Crossings Predicted by Poisson Model for Protection Type 3 175 Figure 5.4: Number of Crossings Predicted by Poisson Model for Protection Type 4 175 Figure 5.5: Number of Crossings Predicted by ZIP Model for Protection Type 1 182 Figure 5.6: Number of Crossings Predicted by ZIP Model for Protection Type 2 182 Figure 5.7: Number of Crossings Predicted by ZIP Model for Protection Type 3 183

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Figure 5.8: Number of Crossings Predicted by ZIP Model for Protection Type 4 183 Figure 5.9: Flow Diagram of Developing Empirical Bayesian (EB) Model 189 Figure 5.10: Flow Diagram of Better-Fit Poisson Model Building Process (Step 1) 204 Figure 5.11: Flow Diagram of Better-Fit NB Model Building Process (Step 2) 205 Figure 5.12: Flow Diagram of Comparing Poisson and NB Models (Step 3) 206 Figure 5.13: Flow Diagram of Best-Fit EB Model Building Process (Step 4) 207 Chapter 6: Figure 6.1: Flow Diagram of Developing Safety Risk Index (SRI) Model 278 Figure 6.2: Identifying Safety Status of Grade Crossings by Safety Risk Index Curve 279 Figure 6.3: Safety Risk Index Curves with Different SRI Values 280 Figure 6.4: Estimating Threshold Value for Black-Spots Identification 282 Figure 6.5: Number of Black-Spots by Protection Types Vs Standardized Score of SRI 283 Figure 6.6: Safety Risk Index Vs Percentage of Protection Type 1 Accidental Crossings 285 Figure 6.7: Black-Spots Identification in Protection Type 1 Grade Crossings 285 Figure 6.8: Safety Risk Index Vs Percentage of Protection Type 2 Accidental Crossings 286 Figure 6.9: Black-Spots Identification in Protection Type 2 Grade Crossings 287 Figure 6.10: Safety Risk Index Vs Percentage of Protection Type 3 Accidental Crossings 288 Figure 6.11: Black-Spots Identification in Protection Type 3 Grade Crossings 288 Figure 6.12: Safety Risk Index Vs Percentage of Protection Type 4 Accidental Crossing 289 Figure 6.13: Black-Spots Identification In Protection Type 4 Grade Crossings 290 Figure 6.14: All 447 Black-Spots Identified in Four Protection Type Grade Crossings 291 Figure 6.15: Graphical Demonstration on Comparison of Black-Spots to Crossings Ranked 306 Figure 6.16: Three Cluster Regions of 447 Black-Spots in All Protection Types 308 Chapter 7: Figure 7.1: Flow Diagram for Impact Analysis on Models Developed in the Study 311 Figure 7.2: Effect of AADT on Collision Prediction by Protection Type 313 Figure 7.3: Effect of Number of Traffic Lanes on Collision Prediction by Protection Type 314 Figure 7.4: Effect of Highway Speed on Collision Prediction by Protection Type 315 Figure 7.5: Effect of Daily Train Traffic on Collision Prediction by Protection Type 316 Figure 7.6: Effect of Number of Main Tracks on Collision Prediction by Protection Type 317 Figure 7.7: Effect of Train Speed on Collision Prediction by Protection Type 318 Figure 7.8: Effect of AADT on Predicted Collision Ratio 319 Figure 7.9: Effect of Number of Traffic Lanes on Predicted Collision Ratio 320 Figure 7.10: Effect of Highway Speed on Predicted Collision Ratio 321 Figure 7.11: Effect of Daily Train Traffic on Predicted Collision Ratio 322 Figure 7.12: Effect of Number of Main Tracks on Predicted Collision Ratio 323 Figure 7.13: Effect of Train Speed on Predicted Collision Ratio 324 Figure 7.14: Effect of Occupants in Vehicle on Consequences Prediction by Protection Type 325 Figure 7.15: Effect of Train Speed on Consequences Prediction by Protection Type 326 Figure 7.16: Effect of AADT on Estimation of SRI by Protection Type 328 Figure 7.17: Effect of Number of Traffic Lanes on Estimation of SRI by Protection Type 329 Figure 7.18: Effect of Highway Speed on Estimation of SRI by Protection Type 330 Figure 7.19: Effect of Occupants in Vehicle on Estimation of SRI by Protection Type 331 Figure 7.20: Effect of Daily Train Traffic on Estimation of SRI by Protection Type 332 Figure 7.21: Effect of Number of Main Tracks on Estimation of SRI by Protection Type 333 Figure 7.22: Effect of Train Speed on Estimation of SRI by Protection Type 334 Chapter 8: Figure 8.1: 447 Basic Black-Spots Identified in All Protection Types of Grade Crossings 343 Figure 8.2: Worst Black-Spots Identification in All Protection Types of Grade Crossings 344 Figure 8.3: Number of Worst Black-Spots Identified as per SRI Threshold Value Selected 345

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Abbreviations

AIC Akaike's Information Criterion ALARP As Low As Reasonably PracticableAS / NZS Australian and New Zealand StandardsATC Australian Transport Council ATP Automatic Train Protection AADT Average Annual Daily TrafficDOT Department of Transportation EB Empirical BayesianEFS Equivalent Fatality ScoreEC European Countries ETSC European Transport Safety Council FRA Federal Railroad AdministrationGLM Generalised Linear ModellingGOF Goodness-of-FitHRGC Highway-Railway Grade Crossings ITSRR Independent Transport Safety and Reliability Regulator LC Level Crossing LR Linear RegressionNB Negative BinomialOHS Occupational Health & SafetyPPE Personal Protective Equipment RSSB Rail Safety & Standards BoardRC RailCorpRSA Railway Safety ActSMS Safety Management SystemSRI Safety Risk IndexSPAD Signal Passed at Danger UN United Nation USDOT US Department of Transportation WD Warning DeviceWCA WorkCover AuthorityZIP Zero-Inflated Poisson

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Nomenclature

iP Risk score due to probability for thi hazard

iC Risk score due to consequence for thi hazard

iE Risk score due to exposure for thi hazard

SRI Safety Risk Index λ Poisson parameter (e.g. Accident occurrence rate) 2s Sample variance

_

y Sample mean

a, ib

Regression parameters

iZ ith reference variable

iR Measure of risk for a class of events X Expected accident frequency at a grade crossing Y Estimated consequences (equivalent fatalities) at a grade crossing ℜ Estimated safety risk index (SRI) value at a grade crossing

oℜ Critical (or threshold) safety risk index value

1ω, 2ω Weighting factors used in EB models Κ Over-dispersion parameter used in EB models

Var (Y) Variance of accidents )(ˆ YE Estimated mean value of accidents from Poisson / NB models

y Actual number of accidents from the accident history ),(ˆ yYE Refined estimation of accidents from EB models

)|(ˆ YCE Predicted number of equivalent fatalities by Poisson / NB Models )]|(),|[(ˆ YCYCE Refined estimation of equivalent fatalities from EB models

e Exponential function Ln Logarithm function

2R Values of determination coefficient in regression models 2χ Chi-square statistic

DT Daily Train Movement AADT Annual Average Daily Traffic MTTS Maximum Timetable Train Speed

HS Highway Speed MT Number of Main Tracks TL Number of Traffic Lanes

TCA Track Crossing Angle TOV Total Occupants in Vehicle EFS Equivalent Fatality Score FAT Number of fatalities INJ Number of Injuries PVD Property and vehicle damage in dollars

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Abstract

In the global view, among other rail safety issues, highway-railway accidents

continue to be a major problem from both public health and socio-economic

perspectives. It is noted that many research studies have been conducted in the past

in relation to developing appropriate models to assess the road traffic safety through

collision prediction, but a considerable amount of work has been carried out only

regarding safety at “highway-railway” grade crossings.

The primary objective of this study is to provide an improved method for rail safety

appraisal at “railway-highway” grade crossings through the development and

application of suitable safety risk scores (called ‘Safety Risk Index’) with a

combination of both accident frequency and accidental consequences prediction

models generated for crossings, and also by using these safety risk scores to identify

the worst or most dangerous locations. The Safety Risk Index (SRI) is a simple

composite index, which can measure, compare and rank safety levels at different risk

situations and locations. These safety risk scores are designed to generate an overall

grade crossings safety risk, which is based on the combination of three basic risk

elements - namely the exposure of the crossing users, the probability of an accident

taking place, and the severity of consequences should an accident occur. This method

facilitates the assessment of the safety risks at grade crossings and also ranks,

identifies and prioritises the worst performing crossings or the problematic crossings

(Black-Spots). This model is very simple and easily understood by those with

different levels of knowledge on safety. The SRI index based on quantitative

methods and developed in this study seems very promising and has great potential to

be a major tool for safety risk assessment at grade crossings in various countries.

The secondary objective of this study is to provide an index with a single meaningful

value for assessing the risk at grade crossings, through the gathering and analysis of

data, information and knowledge (from various data sources) on rail safety. The

research study also establishes appropriate statistical methodologies in order to

develop and to construct a quantitative model for risk assessment.

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Chapter 1

Introduction to the Research

1.0 Introduction

In the broader aspect of safety associated with various modes of transport, in

particular with rail transport, safety at railway crossings is a major area for concern

with an increasing number of accidents across various railroad infrastructures. In

recent times, the safety of rail crossings and associated safety risk assessments

across many situations of road-rail crossings have attracted increasing attention.

However, the need for further research in this area, in particular developing

comprehensive safety risk assessment models, is warranted with the increasing

demand for improved safety which can contribute to improved public health and

socio-economic benefits.

This chapter introduces the research topic and briefly discusses the initiative of the

research. It briefly presents an outline structure of the thesis and explains the

reasons why this study is of interest. The aim of the study is also highlighted and a

brief description of the developing concept of a risk assessment model (Safety Risk

Index) is discussed. It initially provides the basic definition of safety and risks and

briefly describes Occupational Health and Safety (OHS) in general industries. It

provides an overview of general safety management systems used in industries. In

addition, it elaborates the background of the existing potential of rail safety risks and

the overview of rail safety management systems. It also describes the objectives of

the research study and lists the benefits achieved in relation to this research. Finally

it outlines the structure of the thesis in detail.

1.1 Overview of Risk and Occupational Health & Safety

Human life is often put at risk when performing various activities in different ways.

Basically, risk is the chance that a safety hazard will result in an accident which

causes casualties such as loss of life, injury or property damage. Statistically, risk is

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the probability of an untoward event or unfavourable consequence of an event. This

truism may have very distinct meanings in the individual locations and populations

of today’s world. Australian / New Zealand Standard 4360 (2004) defines

‘acceptable risk’ as “An informed decision to accept the consequences and the

likelihood of a particular risk”.

In order to understand what safety involves, it is important and necessary to know the

nature of hazards. A hazard is an activity or combination of activities or set of

circumstances which could produce an accident with the potential to harm life, health

or property. Hazard identification is the process of identifying all risks in the

workplace. Hazards are the main cause of occupational health and safety (OHS)

problems. Therefore, finding ways of eliminating hazards or controlling the

associated risks is the best way to reduce injury and illness. When attempting to

interpret what ‘safety’ means, an ambiguous situation is created. However,

Australian / New Zealand Standard 4801 (2001) provides meaning to the term

‘safety’ as “A state in which the risk of harm (to persons) or damage (to properties)

is limited to an acceptable level”.

Given the very close relationship between safety and accidents, the literature

suggests that the level of safety is inversely proportional to the number of accidents

(Dixit 2007, p.1). Safety at workplaces and also in public places continues to be one

of the major emerging concerns and issues in most developing countries. Measuring

safety is needed to assess the level of safety, and thereby to identify and improve

processes and procedures outlined in the safety management systems. Most of the

current safety accreditation procedures appear to allow the tolerance of some risks. In

various industries, employees today face a wide array of potential risks to their health

and well-being. Some hazards are reasonably apparent, whilst others are often more

insidious. Hazards are the prime identifiable cause of occupational health and safety

problems (WorkCover-NSW 1996, p.7). Some examples of occupational hazards are:

• Trip hazards in a passage or corridor;

• Lifting things in an unsafe manner;

• Using chemicals incorrectly;

• Handling of flammable liquids in the presence of ignition sources;

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• Loose asbestos released during demolition work which has the potential to

cause lung cancer;

• Noise from an uninsulated chainsaw which can reach levels of up to 110 dB

with the potential to seriously damage hearing;

• Badly designed shovel (for example, with a short handle and very large

blade) which has the potential to cause back injury;

• Waste oil from an engine which has the potential to damage workers' health

through skin absorption, due to its carcinogenic properties.

Occupational Health and Safety (OHS) issues arise not only from physical and

chemical problems but also from other features of the operating conditions such as an

employee’s work experience. Under the OHS Acts and Regulations provided in

various countries, the employer has ultimate responsibility to ensure that a safe

workplace is maintained. To meet this requirement, employers must ensure that some

forms of safety systems are in place and that responsibility has been allocated to

managers, supervisors and workers in the organisation. In the meantime, all

employees should take responsibility for their own health and safety and for others

who may be affected by acts or omissions on their part. Safety responsibility should

be part of the daily functions of everyone in the workplace. To assign the safety

responsibilities the following are put in place for workers (NT WorkSafe 2003):

• Incorporate health and safety responsibilities into job descriptions for all

workers and encourage workers to identify unsafe work situations;

• Responsibilities and accountabilities should be assigned for such things as

induction training, first aid, emergency procedures and workplace

inspections;

• Ensure that workers fully understand their responsibilities for health and

safety. Using induction, adequate education and training programs can

achieve this aim.

A major challenge for many employers would be managing safety to meet the

specified requirements set up by government and safety regulators. In recent times,

safety management systems have been developed for managing the above challenges

with some success across various industries.

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1.2 Safety Management System (SMS)

In general, a safety management system (SMS) is considered to be a businesslike

approach to safety. It is a systematic, explicit and comprehensive system for

managing safety risks. As with all management systems, a SMS provides for goal

setting, planning, and measuring performance. A SMS is woven into the fabric of an

organisation (Civil Aviation Safety Transport Canada 2001, p.1). In this regard, SMS

is implemented across various functional areas of an organisation, aiming to manage

and control the potential risks at workplaces. With the increased use of SMS across

various industries and organisations, it has become part of the culture, the way

people do their jobs. NT WorkSafe (2003, p.6) states that ‘Safety management is

described as a set of actions or procedures relating to health and safety in the

workplace, put in place and actively endorsed by management to achieve the

following’:

• Identification, assessment and elimination or control of all workplace hazards

and risks;

• Active involvement in health and safety matters with managers and workers

working together both formally and informally to improve health and safety;

• Providing necessary information and training for people at all levels so they

can effectively meet their responsibilities; and

• Designing and implementing company goals about health and safety.

Further, a SMS provides an organisation with the capacity to anticipate and address

safety issues before they lead to an incident or accident. A SMS also provides

management with the ability to deal with accidents and near misses effectively so

that valuable lessons are learnt and changes implemented to improve safety and

efficiency (Civil Aviation Safety Transport Canada 2001, p.5). The SMS approach

reduces losses and improves productivity. The basic safety management process is

generally accomplished with major elements of events and functions such as:

• A safety issue / concern is raised, a hazard is identified, or an incident /

accident happens;

• The concern / event is reported or brought to the attention of management;

• The event, hazard, or issue is analysed to determine its cause or source;

• Corrective action, control or mitigation is developed and implemented; and

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• The corrective action is evaluated to make sure it is effective. If the safety

issue is resolved, the action can be documented and the safety enhancement

maintained. If the problem or issue is not resolved, it should be re-analysed

until it is resolved.

When an organisation develops a safety management policy and associated

procedures, they have to fit into the organisation in many ways. For example, safety

management has to be comprehensive, but should not be more complex than the rest

of the company's management program. Safety management must be compatible, and

preferably, integrated into the overall management scheme. A list of the

organisation’s safety system procedures is helpful to managers who want to know

more about how to make safety management a reality. Most items in this list will be

familiar to managers. They are already part of the safety landscape. The fundamental

changes are concerned with roles and accountability of company's management and

the regulator.

1.3 Background of Rail Safety Risk Potentials and Rail SMS

United Nations (2000, p.1) states that each year, accidents at level crossings not only

cause the deaths of or serious injuries to many thousands of road users and railway

passengers, but also impose a heavy financial burden in terms of interruption of

railway and road services and damage to railway and road vehicles and property.

This leads to the following phenomena:

• Many billions of dollars are paid in medical costs and disability payments;

• Medical insurance premiums are increased to meet the rising costs;

• Capacity of operations and productivity is decreased;

• Heavy loss of lives and human suffering;

• Inconvenience caused to the people injured, to others and to the environment.

The Rail Safety & Standards Board (RSSB) in the United Kingdom claims that rail is

still one of the safest forms of public transport and is nine times safer than travelling

by car. However, the railway occurrences and the rise in accidental consequences

(including fatalities, injuries and property damage) sustained by passengers, railway

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employees and public in recent years provide a stark reminder of the potential for

hazards in railway systems worldwide. Railway occurrences include both:

• Accidents affecting life and property of passengers, public and employees;

and

• Incidents that do not result in accidents directly but have the potential to do

so (known as ‘near miss accidents’).

Railway occurrences (accidents and incidents) don’t just happen, nor are occurrences

completely accidental in nature. There may be many factors which contribute to the

railway occurrences, caused by the failure of one or more safety components of the

railway system. Identifying, prioritising and targeting the hazard potentials and

developing mitigative initiatives and controls can achieve the prevention of such

occurrences. In order to improve rail safety, railway authorities and safety agencies

keep continuously employing various rail SMS in several countries. These systems

are designed to enhance the quality of safety performance for the rail passengers,

public and rail employees.

Therefore, the Rail SMS is important in ensuring rail safety. It provides a holistic,

systematic and optimal way of managing and controlling rail safety risks to achieve

desired safe outcomes in a sustainable way. Britain’s main line railways have

become increasingly safe in recent years (Rail Safety and Standards Board 2006). At

the same time, the number of passengers is rising at an unprecedented rate, freight

traffic has grown and is set to expand even further, and performance is improving.

All this bears out what the Rail sector has always known - that high standards of

performance and safety are inextricably linked. It provides what passengers and

customers expect while creating the essential condition for growth in the traffic. As

the authority for maintaining safety, the Rail sector needs to assure itself and the

community (the public, passengers and employees) that the safety risks are being

managed to levels that are “As Low As Reasonably Practicable” (ALARP).

There are currently different approaches (national and international) to railway

safety, different targets and methods applied. Technical standards, the rolling stock

and the certification of staff and railway undertakings differ from one country to

another and have not been adapted to the needs of an integrated Rail SMS. However,

the world railway safety system covers safety requirements for the system as a

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whole, including infrastructure and traffic management, and the interaction between

railway undertakings and infrastructure senior managers. It also focuses on the

establishment of common safety indicators in order to assess that the system

complies with the common safety targets and facilitates the monitoring of railway

safety performances. In general, the Rail SMS system has been developed to meet

overall needs based on best international knowledge and practices. A number of

initiatives taken under the Rail SMS have led to increased safety awareness and the

application of a structured, proactive approach to safety. Through external

benchmarking and external SMS reviews set up by the Australian/New Zealand

Standards 4801 (2001), the SMS is reinforced to strive for continuous improvement.

Based on state-of-the-art knowledge, international best practices and its own

experience, the Rail sector’s SMS is continuously being upgraded to meet the

challenges and needs of a modern, safe mass transit railway.

EUROPA (2004) states that safety rules and standards, such as operating rules,

signalling rules, requirements on staff and technical requirements applicable to

rolling stock, have been devised mainly nationally. Under the regulations currently in

force, a variety of bodies deals with safety. These national safety rules, which are

often based on national technical standards, should gradually be replaced by rules

based on common standards, established by technical specifications for

interoperability. The new national rules should be in line with current legislations

and facilitate migration towards a common approach to railway safety. In this way,

the Rail sector aims to ensure that:

• Railway safety is generally maintained and continuously improved, taking

into consideration the development of current legislations;

• Safety rules are laid down, applied and enforced in an open and non-

discriminatory manner;

• Responsibility for the safe operation of the railway system and the control of

risks associated with it is borne by the infrastructure managers and railway

undertakings;

• Information is collected on common safety indicators through annual reports

in order to assess the achievement of the common safety targets and monitor

the general development of railway safety.

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One major element of SMS is to develop appropriate methodologies to assess the

safety risk in various operating sectors of railways. One of the major sectors urgently

warranting safety evaluation is the interface of railway and highway. This safety

evaluation includes a quantitative risk assessment procedure to determine the annual

collective risks due to potential accident scenarios from level crossings.

1.4 Significance of the Study

Rail Safety and Standards Board (2004, p.1) states at the outset that "Level Crossing

Risk is likely to become the largest category of train accident risk on the National

Rail network in Great Britain. It is also a significant risk for road users and

pedestrians”. Safety at level crossings is also one of the most serious safety issues

faced by the rail industry in Australia. Sochon and Piamsa-Art (2007, p.1) states that

approximately 100 level crossing crashes occur between a road vehicle and a train

each year and about 8% of these crashes result in deaths. In addition, about 22

pedestrians die each year while crossing railways on public streets. Fatalities at level

crossings are only a small proportion of the national road toll but a major contributor

to the rail toll. A typical railway level crossing in Australia is shown in Figure 1.1.

Figure 1.1: A Typical Railway-Highway Crossing in Australia

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In recent times, the significance of level crossing safety has been highlighted in

several studies. For example, a major trend has recently emerged involving heavy

vehicles (trucks) colliding with trains and causing catastrophic damage to those trains

and the people on board. In the period between January 2006 and June 2007, there

were 11 level crossing crashes involving heavy vehicles. Tragically, 17 lives were

lost. More than $100 million in damages resulted. These major incidents include the

Kerang crash, where 11 lives were lost, and the Lismore crash, where there was one

fatality and more than $25 million in damages resulted (Sochon & Piamsa-Art 2007,

p.1). Figure 1.2 shows the consequences of a level crossing major accident which

occurred in Lismore (Australia) in May 2006. Management of safety at level

crossings falls upon individual jurisdictions. Each jurisdiction manages its own

initiatives such as level crossing infrastructure upgrades and the development of

modelling techniques to identify dangerous crossing locations. By working in

partnership, the rail and road authorities can be drawn upon as necessary, allowing

the development and delivery of better safety projects.

Figure 1.2: Outcome of a Major Accident at Level Crossing (Lismore, Australia 2006)

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In the global view, among other rail safety issues, railway-highway accidents

continue to be a major problem both from public health and socio-economic

perspectives. These collisions are a source of concern for regulators, railway

authorities and the public. For example, each year in the USA, about 363 people lose

their lives and about 1,034 people are injured as a direct result of crossing collisions

occurring at the annual rate of 2,980 approximately (USDOT FRA accidents

database, 2005).

It is noted from the literature that many research studies have been conducted in the

past in relations to developing appropriate collision models to assess road traffic

safety, but very little work has been carried out regarding safety at “highway-

railway” grade crossings. Hence the primary aim of this study is to provide an

improved method for rail safety appraisal through the development and application

of suitable accidents and consequences prediction models for grade crossings and

also by using these models to identify the worst or most dangerous locations (black-

spots). The research involving quantitative analysis is designed and conducted using

a set of secondary data comprising of 209,975 grade crossings selected from all

states in the USA. The proposed model for prediction of accidents and consequences

at grade crossings and its parameters is a combination of a wide range of traffic and

geometric characteristic information together with the corresponding accident data

for each crossing for the five-year period 2001-2005. Potential explanatory variables

were tested and largely identified from initial analysis of the accident characteristics

and associated factors. Generalized Poisson, Negative Binomial and Empirical

Bayesian Linear models for predicting both accidents and consequences were

developed and evaluated separately for the grade crossings with different protection

types. By combining these two predictions, a single measurable index (Safety Risk

Index) is formed and estimated to assess and to prioritise the grade crossings.

1.5 Objectives of the Study

The major objective of this research is to provide a strong basis for the initial process

of developing an appropriate methodology on safety improvement at railway-

highway grade crossings. This methodology is an integral part of a comprehensive

safety management program, which consists of six interconnected steps:

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• Developing separate models for prediction of accidents and consequences at

crossings;

• Identifying crossings where the potential risk of accidents is unacceptably

high;

• Identifying crossings where the potential risk of consequences is

unacceptably high;

• Developing a single composite index (Safety Risk Index) using the prediction

of accidents and consequences to assess and prioritise the potential risk at the

crossings;

• With the estimated values of Safety Risk Index, identifying 'black-spot

crossings' where the overall potential risk is unacceptably high; and

• Assisting in the development of comprehensive safety intervention programs

and guidelines at the state and national levels that includes prioritisation of

countermeasures at high-risk crossings by reviewing the causes of accidents

and available control measures at these locations.

The other objectives of this study is to gather, integrate and summarise available

information, data and knowledge on rail safety from various sources by meaningful

and measurable indicators, which can then be converted into a single meaningful

value for assessing the risk at grade crossings. The research study also establishes

appropriate statistical methodologies in order to develop and to construct a

quantitative model for risk assessment. It is expected that this generic model is

comprehensive and easily understandable for those with different levels of

knowledge on safety. The model is useful not only to calculate risk assessments but

also to rank rail safety at different grade railway-highway crossing locations. It is

therefore believed that the model is capable of increasing awareness of rail safety

issues and problems among the rail safety policy makers, rail users and road users.

1.6 Target of the Study

The target of this study is to explore new opportunities to enhance the evaluation

techniques in risk assessment used in support of effective rail SMS. In order to

achieve the goal, this research is designed to develop a set of statistical

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methodologies to combine appropriate key performance indicators of rail safety into

a single value of quantitative index. The study provides an improved method for

safety appraisal at railway-highway grade crossings through the development and

application of suitable safety risk scores (called ‘Safety Risk Index’) with

combination of both accident frequency and accidental consequences prediction

models generated for crossings. The Safety Risk Index is a simple composite index,

which can measure, compare and rank safety levels at different risk situations and

locations. These safety risk scores are designed to generate an overall grade crossings

safety risk, which is based on the combination of three basic risk elements, namely

the exposure of the crossing users, the probability of an accident occurring, and the

severity of consequences should an accident occur. This method facilitates not only

the assessment of the safety risks at grade crossings but also identifies and prioritises

the worst performing crossings. These problematic crossings are called ‘black-spots’.

1.7 Benefits of the Study

Railway-highway crossing safety enhancement programs typically have three types

of benefits in relation to financial and socio-economic perspectives. The first is

clearly that of minimising (if not completely eliminating) collisions between trains

and highway vehicles at level crossings. The second benefit is minimising (if not

eliminating) the deaths, injuries, property damage and human suffering associated

with these collisions. The third is that of minimising the delays to both rail and road

traffic at level crossings as a result of imposed speed restrictions on rail operations

and of excessive barrier closure times against highway traffic. The first and second

benefits are considered as primary benefits for a country and its people while the

third provides a secondary benefit.

In this study, the primary benefits (as explained above) are gained through the

development of an improved method to assess safety risks at the different level

crossing locations and utilising the estimated single Safety Risk Index (SRI) scores.

The SRI is developed using the prediction of accident frequency and consequences

models. With the estimation of SRI scores, safety risks at the different level crossing

locations can be assessed and compared directly between them. One major advantage

in developing the Safety Risk Index is to come up with a comprehensive set of risk

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exposure and severity indicators which includes the maximum available major

parameters in rail safety instead of considering a few isolated indicators such as

accident frequency rates. The SRI index therefore captures a broad view and picture

compared to the traditional models developed in rail safety. The Index can be useful

for researchers who work on safety assessment analysis of level crossings. It may

also be useful to railway and highway operating organisations, as the index indicates

the scale of current issues and problems that they were perhaps not aware of.

In addition, government policy makers can use this index to identify and prioritise

the most dangerous crossing locations (black-spots) in a country and to develop

appropriate policies, strategies and intervention programs in order to minimise the

risks to as low a level as possible at these worst locations. However, there may be

some issues in the quality of risk assessment. For example, incomplete information

or deteriorating quality and quantity of the data (such as accidents frequency,

accidental consequences, and train and vehicle movements) may jeopardize the

success of safety evaluation in the SMS.

Overall, the author strongly believes that this study provides useful insights into

safety at railway level crossings and a holistic approach for assessing safety risk as

part of a rail SMS, particularly risk management at different types of level crossing

locations. The quantitative risk analysis techniques developed in this study can be

applied in the rail SMS in order to indicate which grade crossing locations should be

accorded high priority for implementation of safety intervention programs, purely on

the basis of their risk-minimising potential.

1.8 Limitations of the Study

There are some limitations associated with the research study undertaken and

reported here. Firstly, this study examines the accident risks at railway-highway

grade crossings. Accidents within station or yard premises and non-crossing

locations, those due to trespassing or suicides, and near miss accidents are not

included in this study.

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Secondly, it is noted that the number of annual accidents and the annual accidents

frequency rate for ‘Public’ railway-highway crossings are exceptionally high values

(as shown in Figure 4.8 in Chapter 4) in comparison with other types of crossings

such as ‘Private’ and ‘Pedestrian’ level crossings. Given the significance of public

railway-highway crossings with large number of accidents, this research study is

therefore focused on analysing accidents aspects of ‘Public’ railway-highway

crossings.

Finally, the development of risk assessment models is based on the US grade

crossings accidents statistical data rather than data in Australian context. This is due

to unavailability of data across all necessary indicators which are required to assess

risk at grade crossings in Australian rail networks. Even though the new approach

developed in this study is applicable for risk assessment at grade crossings in any

country, the methodology generated is considered more appropriate in the US

environment, since the US grade crossings accidents data were used to develop the

models.

1.9 Structure of the Thesis

The research study undertaken and reported herein falls within broader areas of

safety management systems and procedures. At the outset of this research, SMS and

procedures used in general industries were initially identified and discussed.

Furthermore, specific SMS procedures used in rail industry were then analysed. The

risk management system (one of the major elements of SMS) was selected for further

consideration. The risk assessment process was also recognised as an important part

of a risk management system. Finally, a risk assessment study was conducted on the

grade railway-highway crossings, as safety at these locations becomes one of the

major emerging issues. A brief outline of research areas/topics leading to the

selection of the research topic (Assessing and Prioritising Safety Risks at Interfaces

of Railway and Highway) is schematically shown in Figure 1.3.

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INDUSTRIAL SAFETY MANAGEMENT SYSTEMS • Construction Industry • Mining Industry • Manufacturing Industry • Government Administration and Defence Industry • Transport Industry (Railway, Highway etc.) • Agriculture Industry • Education Industry • Wholesale Industry • Retail Industry • Electricity, Gas and Water Supply

RAIL SAFETY MANAGEMENT SYSTEMS • Accident Investigation • Establishing a Safety Reporting System • Accident and Incident Reporting • Safety Audit / Assessment • Risk Management System • Safety Orientation and Recurrent Training • Emergency Response Plan • Documentation • Senior Management Commitment • Safety Policy • Safety Information • Establishing Safety as a Core Value • Setting Safety Goals

RISKS MANAGEMENT SYSTEMS • Hazards Identification • Risks Assessment • Risks Control or Elimination

RISKS ASSESSMENT • Risks Exposure • Likelihood / Probability of Event • Consequences of Event

“Assessing and Priorit ising

Safe ty Risks at Interfaces of Railw ay and H ighw ay”

Figure 1.3: Logical Flow of Research Areas Leading to the Thesis Topic

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The logical flow of chapters of the thesis is shown in Fig 1.4. There are eight

chapters organised to present the research work carried out. As indicated earlier, this

chapter (Chapter 1) briefly introduces the research work carried out, including the

importance of the selected topic and reasons why this study is of interest. It also

provides the basics of a railway SMS, an overview of current railway safety issues,

the goals and objective targets set out for the research and the point of departure.

Chapter 2 describes in greater detail the current railway SMS and safety issues, and

expands on the research topic. The chapter describes how rail safety concerns

everyone and all aspects of safety. It also reviews the literature on similar previous

studies. Chapter 3 outlines the research methodology that is adapted to develop the

appropriate statistical model in the study. Various rail safety problems and all micro-

level factors that could contribute to rail accidents are discussed. Key performance

indicators are then identified. Finally, an appropriate methodology is developed to

combine different key performance indicators and to assess the rail safety risks.

Chapter 4 presents a procedure and associated steps for extracting and utilising rail

accident data and inventory information to evaluate rail safety risks through risk

assessment models. Chapter 5 describes the development of appropriate models for

predicting accident frequencies and consequences. It explains the theoretical

framework of the model with the support of the key performance indicators, which

were identified in the previous chapter. It also provides the process of validating the

models developed. Chapter 6 describes and presents a single composite risk index

(Safety Risk Index) to assess and prioritise the rail safety performances at grade

crossings using the predictions obtained in the previous chapter. Chapter 7 is

concerned with sensitive analysis work on the models to identify and discuss the

influences of relevant factors on prediction of accident frequencies, consequences

and safety risks. Conclusions are drawn in Chapter 8 through study findings and

discussions shown in the early chapters. This chapter discusses the contributions and

the outcome from this study. It also clearly indicates the benefits and limitations of

the study. In this chapter, an indication of relevant future research work, which may

extend to the contributions made by this research study, is also supplied.

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Figure 1.4: Flow Diagram for Developing Structure of the Thesis

CHAPTER 1 :

Introduction to the Research

CHAPTER 2 :

Literature Review

CHAPTER 3 :

Research Methodology

CHAPTER 5 :

Development and Validation of Grade CrossingAccidents and Consequences Prediction Models

CHAPTER 7 :

Impact Analysis on Risk Assessment Models

CHAPTER 8 :

Conclusions and Recommendations

CHAPTER 4 :

Data Collection and Consolidation

CHAPTER 6 : Development of Safety Risk Index (SRI) for

Risks Assessment at Grade Crossings

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Chapter 2

Literature Review

2.0 Introduction

Rail safety management is one of the major challenges in the broader management of

safety and risks of rail operations. Given the rapid growth in infrastructure

development, and the increasing demand for rail transport (both passenger and

freight), rail safety management is constantly aiming to improve overall safety of rail

infrastructure, in particular rail-road crossings. The focus of this research is to

investigate rail safety management, from a point of view of managing complex

situations of rail crossings across a network. This involves identifying research

problems within the broader rail safety and risk assessment, and managing

complexities of rail crossings across many situations and locations.

The previous chapter provided the scope and background of the research. In order to

investigate rail safety management and associated systems, it is necessary to

consider its implementation within organisational settings. Thus, this chapter

provides a comprehensive overview of the safety management system, the risk

assessment process used in the rail safety management system and the challenges

faced in managing risks in Rail sectors. This chapter also describes the magnitude of

existing rail safety risk issues / problems in details. It provides some typical Safety

Management Systems used in many organisations. It also identifies the major safety

issues and the significance on improving safety at level crossings. Finally the

research problem for this study is broadly articulated.

2.1 Definitions of Terms Used in Relations to Safety In the Safety Management System, important terms are frequently used to describe

the system. The following are some of those terms and their definitions.

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2.1.1 Accidents

An accident is an unwanted event that results in physical harm to people (life or

health) or damage to property. There is a reasonable degree of consensus that an

accident is some kind of unplanned event (Dixit 2007). In general, the term

"incident" describes such events where no injury occurs. However, incidents are

often wake-up calls that can alert employees and supervisors to hazards or risks that

they had not considered before. Every incident is an opportunity to learn valuable

safety lessons. Accidents are directly linked to safety (or lack of it) across various

situations. Thus, the definition of an accident is critically important for any

consideration of safety, in particular when consequences of accidents are estimated /

judged and analysed based on measures of accidents. The definition of an accident

can also influence how one could see accidents (and thereby safety) from a point of

view of what we can see and measure. In general, it can be noted from a process

viewpoint, that accidents have multiple causes such as performing bad practices and

involving risky behaviour. In general, an accident may be defined as an unplanned

event that has the potential to cause adverse consequences due to a combination of

several factors. This nature of process is shown in Figure 2.1.

Combination of Several Factors • Risk

Behaviour • Bad Practices

Adverse Consequences • Risk Potentials • Adverse Effects • Harmful

Consequences

Accident

Figure 2.1: Characteristics of an Event of Accident

It can be noted from the above discussion on accidents and associated safety and

risks that combinations of factors play a significant role in accidents and subsequent

consequences. This is endorsed by the statement: "For the want of a nail, the shoe

was lost; for the want of a shoe the horse was lost; and for the want of a horse the

rider was lost, being overtaken and slain by the enemy, all for the want of care about

a horseshoe nail" by Poor Richard's Almanack (Williamson 2008, p.1). This is very

much true for safety networks as accidents are multi-causal in nature. From a

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prevention point of view safety is concerned with eliminating those causal factors or

interfering with relationship between them.

2.1.2 Hazards

WorkCover - NSW (1996, p.7) states that a hazard is anything with the potential to

harm life, health or property. As hazards are the prime identifiable cause of

occupational health and safety problems, controlling the risk arising from them offers

managers the greatest area of opportunity for reducing injury and illness in the

workplace. Some examples of general hazards at workplaces include:

• Trip hazards in a passage or corridor;

• Lifting things in unsafe manner;

• Using chemicals incorrectly;

• An unguarded gear wheel on a workshop grinding machine which has the

potential to draw a worker's clothing and limbs into the drive of the machine

and cause serious bodily injury;

• Handling of flammable liquids in the presence of ignition sources;

• An unlabelled container of caustic soda which has the potential to cause

severe skin burns if handled incorrectly;

• Loose asbestos released during demolition work which has the potential to

cause lung cancer;

• Noise from an uninsulated chainsaw which can reach levels of up to 110 dB

with the potential to seriously damage hearing;

• A badly designed shovel (for example, with a short handle and very large

blade) which has the potential to cause back injury;

• Waste oil from an engine which has the potential to damage workers' health

through skin absorption, due to its carcinogenic properties;

• Blood in a syringe at a hospital, which has the potential to infect a medical

worker with a disease if the needle punctures the worker's skin.

Hazard identification is the process of identifying all hazards in workplaces. In order

to identify what hazard identification involves, it is first necessary to understand the

nature of hazards. Therefore, finding ways of eliminating hazards or controlling the

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associated risks is the best way to reduce injury and illness. Hazards may arise from

public places or a workplace environment through bad practices. Hazards can arise in

many different ways and can take various forms. In order to be in a position to

properly undertake hazard identification, it is important to understand the sources of

hazards and the forms in which they may arise. Hazard identification involves the

systematic investigation of all potential hazard sources and the recording of hazards

identified. It means that hazard identification is to identify all of the possible ways in

which people may be harmed through work-related activities. Since modern

workplaces are complex and have a range of plants, chemicals and potentially

hazardous work processes, a systematic approach to the identification process is

required. This approach is explained in detail later under the topic Risk Management.

2.1.3 Risks

As discussed in the previous chapter, there are sometimes risks to human life in

performing various activities in inappropriate ways. Basically, risk is the chance that

a safety hazard will result in an accident which causes casualties such as loss of life,

injury or property damage. Statistically, risk is the probability of an untoward event

or the unfavourable consequence of an event. This truism may have very distinct

meanings in individual locations and populations. Australian/New Zealand Standard

4360 (2004) defines ‘acceptable risk’ as “An informed decision to accept the

consequences and the likelihood of a particular risk”. Risk is a concept that denotes

a potentially negative impact to an asset (object, resource, property or human) or to

some characteristic of value that may arise from some present process or future

event. In everyday practice, risk is often used synonymously with the probability of a

loss. Paradoxically, a probable loss can be uncertain in an individual event while

having a certainty in the aggregate of multiple events. Alikhani (2009, p.113) stated

that an engineering definition of risk is generally given as:

accident)per (Losses * accident)an ofty (Probabili =Risk (2.1)

Risk is often estimated based on the probability of an event which is seen as

undesirable. Usually the probability of such an event occurring and some assessment

of its expected harm must be considered in a scenario (an outcome) which combines

the set of risk, regret and reward probabilities into an expected value for that

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outcome. Thus in statistical decision theory, the risk function (R ) of an estimator

δ(x) for a parameter θ, calculated from some observables x; is defined as the

expectation value of the loss function L (Kaye 1988, p.174):

dx )/(x f * (x)) , L( = (x)) ,R( θδθδθ ∫ (2.2)

where:

R  ‐  Risk function

L  ‐  Loss function

x             ‐  Observables

δ(x)  ‐  Estimator

θ            ‐  Parameter of the estimator In scenario analysis, risk is distinct from threat. A threat is a very low-probability but

is a serious event - some analysts may be unable to assign a probability in a risk

assessment because it has never occurred, and for which no effective preventive

measure (a step taken to reduce the probability or impact of a possible future event)

is available (Franck 2008). The difference between risk and threat is most clearly

illustrated by the precautionary principle which seeks to reduce threat by requiring it

to be reduced to a set of well-defined risks before an action, innovation or

experiment is allowed to proceed. A risk is defined as a function of three variables:

• Probability that there is a threat;

• Probability that there are any vulnerabilities; and

• Potential impact.

If any of these variables approaches zero, the overall risk approaches zero (Franck

2008). The systematic procedure in managing risks is called risk management. Some

industries manage risk in highly quantified and numerate ways. These include the

nuclear power and aircraft industries, where the possible failure of a complex series

of engineered systems could result in highly undesirable outcomes. The usual

measure of risk ( iR ) for a class of events (i) is given by the equation of:

iii CPR *= (2.3)

where iP and iC are probability and consequences of the event respectively. The total

risk (R ) is then the sum of the individual class-risks and is given by the equation of:

∑∑ == iii CPRR * (2.4)

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Measuring risk is often difficult, rare failures can be hard to estimate, and loss of

human life is generally considered beyond estimation (Sommer 2008). There are

many informal methods used to assess or to measure risk, although it is not usually

possible to directly measure risk. Formal methods such as Event tree analysis, Fault

tree analysis and Reliability analysis measure the value at risk.

2.1.4 Safety

As stated earlier, it is important and necessary to understand the nature of hazards for

examining what safety involves. A hazard is an activity or combination of activities

or set of circumstances which could produce an accident with the potential to harm

life, health or property. Hazards are the main cause of occupational health and safety

(OHS) problems. Therefore, finding ways of eliminating hazards or controlling the

associated risks is the best way to reduce injury and illness. When attempting to

interpret what safety means, an ambiguous situation can be created. However,

Occupational Health and Safety Management System (Australian/New Zealand

Standard 4801, 2001) describes term ‘safety’ as “A state in which the risk of harm

(to persons) or damage (to properties) is limited to an acceptable level”.

In mathematical terms, the level of safety is inversely proportional to the number of

accidents (Dixit 2007, p.1). Safety at workplaces and also in public places continues

to be one of the major emerging concerns and issues worldwide (especially most

developing countries). Measuring safety required to assess the level of safety to

identify and improve weak links in SMS. There is a major difference between the

concepts of “Absolute Safety” (a zero tolerance with an imposed duty to guarantee)

and “Reasonable Precautions” (Australian/New Zealand Standard 4801, 2001).

Most of the current safety accreditation processes appear to allow the tolerance of

some risks.

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2.2 Safety Management System (SMS) at Organisational Level

This section focuses on a comprehensive analysis of the current safety management

system (SMS) and practices, the responsibility for which rests with each

organisation. The major objective of SMS is to create a safe workplace environment

free from risk to employees and the public. Good management practices are

fundamental to business success in today’s competitive environment. The key

element is to manage a business professionally by drawing together the areas of

engineering, safety, quality, risk management, personnel and finance. None of these

can be managed in isolation and it requires an integrated approach. Employers have a

‘duty of care’ to provide a safe workplace and systems of work, to consult with

workers and to keep them informed about health and safety matters.

A SMS is defined as “a formal framework for integrating safety into day-to-day

company operations and includes safety goals and performance targets, risk

assessments, responsibilities and authorities, rules and procedures, and monitoring

and evaluation process” (British Columbia Safety Authority 2007, p.1). A SMS is a

tool, which enables organisations to demonstrate in a concrete and visible manner of

their commitment to safety. A SMS is a road-map requiring commitment and a

businesslike approach to safety. It is a systematic, explicit and comprehensive

process for managing safety risks. As with all management systems, a SMS provides

for goal setting, planning, and measuring performance. A SMS is woven into the

fabric of an organisation. It becomes part of the culture, the way people do their jobs.

Safety management can best be described as a set of actions or procedures relating to

health and safety in the workplace, put in place and actively endorsed by

management to achieve the following processes (NT WorkSafe 2003, p.6):

• Identification, assessment and elimination or control of all workplace hazards

and risks;

• Active involvement in health and safety matters with managers, supervisors

and workers working together both formally and informally to improve health

and safety;

• Providing necessary information and training for people at all levels so they

can effectively meet their responsibilities;

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• Designing and implementing company goals and objectives about health and

safety.

A SMS will help organisations in the following ways:

• Market the safety standards of their operation;

• Guard against the direct and indirect costs of incidents and accidents;

• Improve communication, morale and productivity; and

• Meet their legal responsibilities to manage safety.

Civil Aviation Safety Transport Canada (2001, p.i) stated that introducing a

systematic approach to the Safety Management explains how to:

• Involve all staff in safety;

• Develop a positive safety culture;

• Maintain commitment; and

• Assess progress.

In recent years a great deal of effort has been devoted to understanding how

accidents happen in industries. It is now generally accepted that most accidents result

from human error. It would be easy to conclude that these human errors indicate

carelessness or incompetence on the job but that would not be accurate. Investigators

find that the human is only the last link in a chain that leads to an accident. Accidents

may not be prevented by changing people. Accidents may only be prevented by

addressing the underlying causal factors. In the 1990s the term ‘organisational

accident' was coined because most of the links in an accident chain are under the

control of the organisation (Civil Aviation Safety Transport Canada 2001, p.1).

2.2.1 The Four ‘P’ Principles of Safety Management System

The organisational structures and activities that make up a SMS are found throughout

organisations and categorised into four ‘P’ principles (Civil Aviation Safety

Transport Canada 2001, p.2). The system is illustrated by four ‘P’ principles in

Figure 2.2. Every employee contributes to the safety health of the organisation. In

larger organisations, safety management activity will be more visible in some

departments than in others, but the system can be integrated into "the way things are

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done" throughout the establishment. This will be achieved by the implementation and

continuing support of coherent safety policy, which lead to well designed procedures.

Philosophy Procedure Policy Practice

Safety Management

System

Figure 2.2: The 4 ‘P’s Principles for Safety Management System

Philosophy - Safety management starts with Management Philosophy:

• Recognising that there will always be threats to safety;

• Setting the organisation's safety standards; and

• Confirming that safety is everyone's responsibility.

Policy - Specifying how safety will be achieved:

• Provision of clear statements of responsibility, authority and accountability;

• Development of organisational processes and structures to incorporate safety

goals into every aspect of the operation; and

• Development of the skills and knowledge necessary to do the job.

Procedures - What management wants people to do to execute the policy:

• Provision of clear direction to all staff;

• Means for planning, organising and controlling; and

• Means for monitoring and assessing safety status and processes.

Practices - What really happens on the job:

• Following well-designed, effective procedures;

• Avoiding the shortcuts that can detract from safety; and

• Taking appropriate action when a safety concern is identified.

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2.2.2 Safety Culture

An organisation's safety culture is characterised by what its people do at work. The

decisions people make tell us something about the values of the organisation. For

instance, the extent to which managers and employees act on commitments to safety

tells us more than words can about what values motivate their actions. A good gauge

of safety culture is "How they do things around there." A safety culture may be slow

to mature, but, with management support, it can be accomplished. A safety culture is

defined by the following four types of cultures (Civil Aviation Safety Transport

Canada 2001, p.3):

Informed culture

• People understand the hazards and risks involved in their own operation

• Staff work continuously to identify and overcome threats to safety

Just culture

• Errors must be understood but wilful violations cannot be tolerated

• The workforce knows and agrees on what is acceptable and unacceptable

Reporting culture

• People are encouraged to voice safety concerns

• When safety concerns are reported they are analysed and appropriate action is

taken

Learning culture

• People are encouraged to develop and apply their own skills and knowledge

to enhance organisational safety

• Staff are updated on safety issues by management

• Safety reports are fed back to staff so that everyone learns the lessons

A positive safety culture can be encouraged by means of the following:

1. Management ‘practices what it preaches’ regarding safety;

2. Management allocates adequate resources to maintain an operation that is

efficient and safe;

3. Management acknowledges safety concerns and suggestions:

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• Management gives feedback on decisions, even if the decision is to do

nothing;

• If no action is contemplated, that decision is explained; and

• Feedback is timely, relevant and clear.

2.2.3 Organisational Involvement in SMS

There are two ways of thinking about safety. The traditional way is that safety has

been about avoiding costs. In this sense, many aviation organisations have been

bankrupted by the cost of a major accident (Federal Aviation Administration 2009).

This makes a strong case for safety, but the cost of occurrences is only part of the

story. Efficiency is another way of thinking about safety. Research shows that safety

and efficiency are positively linked (Civil Aviation Safety Transport Canada 2001,

p.5). Safety pays off in reduced losses and enhanced productivity. Safety is therefore

good for business based on the preceding discussion. An SMS provides an

organisation with the capacity to anticipate and address safety issues before they lead

to an incident or accident. A SMS also provides management with the ability to deal

effectively with accidents and near misses so that valuable lessons are learnt to

improve safety and efficiency. The basic safety management process could be

accomplished in five major steps as shown in Figure 2.3 (Civil Aviation Safety

Transport Canada 2001, p.5):

1. A safety issue or concern is raised, a hazard is identified, or an incident or an

accident happens;

2. The concern or event is reported or brought to the attention of management;

3. The event, hazard, or issue is analysed to determine its cause or source;

4. Corrective action, control or mitigation is developed and implemented; and

5. The corrective action is evaluated to make sure it is effective. If the safety issue

is resolved, the action can be documented and the safety enhancement

maintained. If the problem or issue is not resolved, it should be re-analysed until

it is resolved.

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Issue Not Resolved

Issue Resolved

1. Reporting Safety Issues, Incidents, Hazards etc.

2. Analyse

4. Evaluate

5. Document

3. Corrective Action

Figure 2.3: The Basic Safety Management System Process

2.2.4 Comparison of Current SM S with Traditional Approach

Safety management systems incorporate the basic safety process, described above, as

part of the overall management of an organisation. The traditional safety approach

depended on an individual safety officer (or department in a larger organisation)

independent from operations management, but reporting to the Chief Executive

Officer of the company. The safety officer of the department had, in effect, no

authority to make changes that would enhance safety. The safety officer or

department's effectiveness depended on the ability to persuade management to act. A

SMS holds managers accountable for safety related action or inaction. The SMS

philosophy requires that responsibility and accountability for safety be retained

within the management structure of the organisation. The directors and senior

management are ultimately responsible for safety, as they are for other aspects of the

enterprise. This is the logic that underlies recent Transport Canada Civil Aviation

regulatory initiatives (Civil Aviation Safety Transport Canada 2001). When they

come into force, the new regulations will require certain aviation organisations to

identify their ‘accountable executive'. This is the person who has financial and

executive control over an entity subject to the regulations. The accountable executive

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is the certificate holder. Should an organisation hold more than one certificate, (e.g.,

an operator who holds an air operator certificate and manages an approved

maintenance organisation) there would be only one accountable executive. The SMS

approach ensures that authority and accountability co-exist.

2.2.5 Major Modules of SMS

When an organisation develops a safety management policy and procedures, they

should fit into the organisation’s environment. The policy and procedures have to be

comprehensive, but should not be more complex than the rest of the company's

management program. Safety management must be compatible, and ideally,

integrated into the overall management program. The following list of some major

modules of SMS will be helpful to the manager who wants to know more about how

to make safety management a reality (Civil Aviation Safety Transport Canada 2001,

p.7).

• Senior Management Commitment;

• Safety Policy / Documental Procedures;

• Recurrent Training;

• Emergency Response Plan;

• Setting Safety Goals;

• Hazard Identification;

• Risk Management;

• Establishing a Safety Reporting System / Safety Information;

• Safety Audit / Assessment;

• Accident and Incident Reporting;

• Investigation; and

• Safety Orientation.

Most of the items in this list are familiar to managers. They are already part of the

safety standard practices in current use. The fundamental changes are concerned with

roles and accountability of management and the regulator.

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2.2.6 Initiatives to Build an SMS

To build a SMS in a systematic and professional way, an organisation needs to

establish a comprehensive SMS by ensuring the following four safety initiatives are

formulated and implemented.

• Developing Employer’s Responsibilities;

• Leadership Skills;

• Communicating Safety Information; and

• Creating Safe Working Environment.

2.2.6.1 Employer’s Responsibilities

Under OHS Regulations the employer has ultimate responsibility to ensure that a

safe workplace is maintained (Australian/New Zealand Standard 4801, 2001). To

meet this requirement, employers ensure that SMS are in place and that responsibility

has been allocated to managers, supervisors and workers in the organisation. Safety

responsibility should be part of the daily functions of everyone in the workplace. To

ensure that health and safety responsibilities have been assigned the following be put

in place.

• Incorporate health and safety responsibilities into job descriptions for all

workers and encourage workers to identify unsafe work situations;

• Responsibilities and accountabilities should be assigned for such things as

induction training, first aid, emergency procedures and workplace

inspections;

• Ensure that all workers fully understand their responsibilities for health and

safety. Using induction and adequate education and training programs can

achieve this aim.

A very important part of any SMS is the consultation process between the employer

and workers. It can be extremely useful for employers to talk things over with their

workers, seek and listen to their advice and ask them for information. Safety

management systems work best if everyone, including management and workers, are

actively involved in their development and implementation. Effective consultation

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can be achieved in many ways and the style that best suits relevant business should

be chosen. Some typical examples are:

Management meetings: Effective health and safety systems rely on good

management practices and therefore safety should be on the agenda for management

meetings and appropriate action taken at these meetings.

Informal meetings: Informal meetings are short meetings held in the workplace

when the need arises, where items of health and safety can be discussed. These can

be used to give a brief explanation of how to use a new piece of equipment, or to

show a safety video.

Shift meetings: These are a very important form of consultation where changes of

shift are involved. Safety issues should be included as a routine item for brief

handover meetings between staff starting and finishing shifts.

Need of Safety committees: Safety committees are a structured style of safety

meeting where representative members meet on a regular basis to discuss and

recommend actions on safety.

2.2.6.2 Leadership Skills

The 3 ‘C’ Elements of Leadership: Management initiatives in an organisation are

not always successful and each time a new idea is introduced people ask whether this

is a worthwhile initiative, or a fad that will pass soon enough. Having a good idea

does not guarantee success. Some good ideas may fail in practice because one or

more of the three critical elements was missing: commitment, cognisance, and

competence. These three "C" elements of leadership will determine, in large part,

whether a SMS achieves its goals and leads to a pervasive safety culture in an

organisation (Figure 2.4).

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Commitment Leadership Cognisance Competence

Figure 2.4: The 3 ‘C’ Elements of Leadership

Commitment: Ability of company leaders to make safety management tools work

effectively in the face of operational and commercial pressures.

Cognisance: The company leaders understand the nature and principles of managing

for safety.

Competence: The Safety management policy and procedures of the company are

appropriate, understood, and properly applied at all levels in the organisation.

2.2.6.3 Communicating Safety Critical Information

An Identification, Assessment and Control process establishes what health and safety

information needs to be communicated to workers (Australian/New Zealand

Standard 4360, 2004). This information should then be distributed in appropriate

ways. Information that should be communicated to workers includes the following

elements:

Nature of the hazards and risks: Workers must be given adequate information on

the hazards and risks they encounter on a daily basis. This is to ensure that they can

take appropriate action to ensure their safety at work and the safety of others. This

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information can come in many forms ranging from material safety data sheets for

chemicals, to product information and equipment operating instructions.

Emergency procedures: Workers must be adequately instructed in appropriate

emergency procedures relevant to their workplace to ensure their safety. All

workplaces will need some form of emergency procedure information, such as fire

drills, emergency evacuation procedures and steps to take if a worker is injured.

Work procedures: All workers must be given adequate information so they can

work safely. Safe working procedures need to be developed and communicated to all

workers. Often incorrect assumptions are made about work procedures, which can

result in accidents. Work procedures need to be documented, regularly reviewed and,

where required, updated to ensure accuracy.

Instruction and training: Instruction and training plays an important role in

ensuring that safe systems of work are effectively achieved and maintained. Some

examples of instruction and training that may be required in our workplace are:

• Induction programs for new or relocated workers;

• Refresher courses to keep workers up to date;

• Workers are trained to use plant and equipment and have appropriate

licences;

• First-aid training, and when there are required changes in the workplace re-

training may be required.

2.2.6.4 Elements of a Safe Working Environment

To achieve the goal of effective safety at workplaces, senior management needs to

identify and to maintain the following elements for safe working environment

(Australian/New Zealand Standard 4360, 2004).

Supervision: Adequate supervision is an integral part of ensuring a safe working

environment. In determining the level of supervision required, the level of instruction

and training provided to workers, together with their knowledge and experience,

needs to be considered.

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Injury management: Work Health legislation requires that injured workers have

access to first aid, fair workers compensation and return to work rehabilitation.

Therefore, managing injuries is an integral part of a SMS.

First aid: Employers must carry out an assessment of first-aid requirements in their

workplace and ensure that appropriate equipment facilities and trained personnel are

available and readily accessible in the workplace.

Workers compensation: A Workers compensation claims record is one measure of

the success of a safety management program. Employers are required to have a

current insurance policy for their permanent employees. Employers should advise

temporary workers, contractors, etc, that they are not covered and they should

consider taking out their own insurance. This could be included in their induction

program.

Rehabilitation and return-to-work : Rehabilitation can include medical treatment,

which reduces the effects of an injury. Occupational or vocational rehabilitation

assists the worker to return to the workplace. Employers should assist in

rehabilitation and return-to-work programs for their workers. Employers are key

players in successful return-to-work programs. Good rehabilitation involves

commitment and consultation. By being actively involved and taking control, we can

reduce claim costs and ultimately premium costs and have a positive effect on morale

in our workplace.

Record keeping: Record keeping is an important tool for employers to monitor the

performance of their SMS. This need not be a complicated task and in some cases, a

simple diary of events, procedure, instructions or the like, may be all that is needed.

Records must be kept as evidence of compliance with legislation. However, many

other benefits can be achieved from good record keeping, as outlined below:

Identification, assessment and control: Records are evidence that legislative

responsibilities have been met. They build a history, which helps with continual

improvement.

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Maintenance and inspection: Records for plant and equipment enable us to

program future maintenance and can improve the resale value by providing a

complete history.

Accident investigation: Records can be used as a source for identifying hazards and

preventing accidents. These should also include records of near misses, as these are

often a clue to a future, preventable accident.

Hazardous Substance Register: This is a collection of material safety data sheets

(MSDS) for all chemicals used at the workplace and is an accessible source of

information for workers. If there is no MSDS, the chemical should not be used. If

dangerous goods are stored or handled, records relating to these activities may also

need to be kept.

Comprehensive personnel records: Identifying personnel by their qualifications,

experience and training:

• Ensures personnel are suitable for a particular task;

• Makes the best use of staff;

• Identifies training needs which helps to obtain the best value for money; and

• Ensures recruitment of the most appropriate staff for company needs.

Safety program evaluation: Accidents increase liability, reduce profit and endanger

the well-being of employees. Effective loss control is critical to an organisation's

success in today's competitive business climate. But what is the best way to reduce

risk? Where should limited resources be directed to have the greatest impact? How

can we be sure that our risk reduction measures are working? These are difficult

management decisions requiring careful evaluation. Research has shown that several

elements influence the safety of an operation. Understanding a company's

effectiveness at controlling risk within each of these areas is critical to identifying

weakness and strengthening one's safety record. Therefore, a comprehensive auditing

system to assist managers in evaluating current environmental, health and safety

management practices has to be developed which: 

• Maximises risk reduction efforts by identifying the strengths and weaknesses

of a safety program.

• Validates effective safety management practices.

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• Is statistically proven to measure loss.

• Quantifiably measures safety performance within an organisation or between

various operations.

• Improves regulatory compliance with environmental, health and safety

requirements.

Effectiveness of control measures: Risk control measures must also be maintained,

e.g. work procedures have to be monitored to ensure they are being followed,

hearing protectors have to be kept clean and checked for damage. All control

measures have to be assessed in order to determine:

• Whether or not they have had the intended effect;

• That no hazards have been created by the control measures.

Effectiveness of process: The process itself should be assessed to ensure it is

effectively managing the risks. For example, a control measure may have failed

because not all hazards were identified, or because the likelihood of a risk was

wrongly assessed. If this is the case, it may be necessary to change the way the

system is implemented in the workplace.

Effectiveness of consultation, information, in struction and training: Assessment

of consultation mechanisms would include whether safety committees are operating

effectively and if workers are really involved in the process of safety. When

considering information, instruction and training we would look at how up-to-date

and relevant they are. Also consider whether the information is reaching all who

need it, e.g. new workers, non-English speakers.

Monitoring and Review: Monitoring and review of the various components of the

SMS must be carried out to see how effective they are.

2.2.7 Measurements on Effectiveness of SMS

A senior management question is “What gets measured to improve safety at

workplaces?” Another question is “How can it be measured?” Top management is

looking for safety initiatives, with a positive impact upon the organisation’s total

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performance (Mathebula 2001, p.7). The management wants initiatives that they can

approve and invest their time in, to effect five key measures:

• Return on Assets (ROA) – Changes in this measurement indicates how an

individual program impacts profitability.

• Value Added per Employee (VAE) – Changes in this measurement reflect

how an individual program impacts on productivity.

• Economic Value Added (EVA) – Changes in this measurement reflect how a

shareholder’s value is created or destroyed by management. EVA has been an

economic toolkit for more than two hundred years. Simply put, EVA is the

measure of corporate performance that differs from most others by including

a charge against profit for the cost of all the capital a company employs. For

example an accident, which results in the destruction of assets, is a value

destroyer and may lead into negative EVA.

• Frequency Rate (FR) and Severity Rate (SR) – Changes in this measurement

reflect lost time due to injuries. It is also valuable to track FR for medical aid

injuries and first aid injuries.

2.3 Risk Management within SMS

Risk management is part of broader SMS and links through key inputs and outputs

such as measuring, or assessing risk and developing strategies to manage it.

Strategies include transferring the risk to another party, avoiding the risk, reducing

the negative effect of the risk, and accepting some or all of the consequences of a

particular risk. Traditional risk management focuses on risks stemming from physical

or legal causes (e.g. natural disasters or fires, accidents, death, and lawsuits). It is

stated that in ideal risk management, a prioritisation process is followed whereby the

risks with the greatest loss and the greatest probability of occurring are handled first,

and risks with lower probability of occurrence and lower loss are handled later

(Kokash & D'Andrea 2006, p.11). In practice the process may be difficult. Balancing

between risks with a high probability of occurrence but lower loss versus a risk with

high loss but lower probability of occurrence can often be mishandled. Intangible

risk management identifies a new type of risk - a risk that has a 100% probability of

occurring but is ignored by the organisation due to a lack of identification ability. For

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example, knowledge risk occurs when deficient knowledge is applied. Relationship

risk occurs when collaboration ineffectiveness occurs. Process-engagement risk

occurs when operational ineffectiveness occurs. These risks directly reduce the

productivity of knowledge workers, decrease cost effectiveness, profitability, service,

quality, reputation, brand value, and earnings quality. Intangible risk management

allows risk management to create immediate value from the identification and

reduction of risks that reduce productivity. Risk management also faces difficulties

in allocating resources. Resources spent on risk management could have been spent

on more profitable activities. Again, ideal risk management minimises spending

while maximising the reduction of the negative effects of risks.

2.3.1 Major Processes in Risk Management

In general, a Risk Management System comprises three major processes as shown in

Figure 2.5 (Australian/New Zealand Standard 4360, 2004). They are:

• Hazards Identification;

• Risks Assessment; and

• Risks Control or Risks Elimination.

1. Hazards Identification

Risk

Management System

2. Risks 3. Risks Assessment Control or . Elimination

Figure 2.5: Three Major Processes in Risk Management System

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2.3.2 Hazard Identification

The Risk Management System emphasises that all employers must ensure that

appropriate measures are taken to identify the hazards and assess the risk to the

health and safety of every person in the workplace (Australian/New Zealand

Standard 4360, 2004). There are a number of ways in which hazards can be

identified in the workplace:

• Walk-through survey compiling a hazards list as we go;

• Check accidents, near misses and workers compensation records;

• Talk to workers, e.g. safety committee meetings, informal meetings;

• Look at how work is done, including manual handling practices such as

lifting, pushing, pulling, moving, etc.; and

• Liaise with experienced people in a similar industry

In the event of an incident, photographing workplace hazards is extremely useful, not

only for recording purposes but also when highlighting issues through discussion at

health and safety committee meetings. The hazards identification process generally

contains the following functions (Australian/New Zealand Standard 4360, 2004).

• Dividing hazard identification into manageable portions;

• Developing an inventory of tasks;

• Analysing tasks;

• Identifying the hazards involved;

• Considering the people factor;

• Aiding hazard identification;

• Hazard identification as ongoing process; and

• Recording hazard identification data

2.3.2.1 Dividing Hazard Identification into Manageable Portions

As identifying every hazard throughout the workplace can be an extremely large and

complex job, the first step is to break this job down into 'bite-sized chunks'. This can

be achieved using the following techniques:

• Breaking the workplace into work sectors or areas (and, if necessary,

breaking down further into zones);

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• Breaking each sector down into tasks;

• Developing a list of likely hazards for the work sector; and

• Analysing the components of each task to identify the individual hazards

present.

2.3.2.2 Developing an Inventory of Tasks

Once the workplace has been divided logically into work sectors (such as the

operations, maintenance sectors etc.) and, if necessary, into zones (such as station

operations, depot maintenance, etc.), a complete inspection of all workplace tasks

should be carried out. This will develop an inventory of all the tasks performed

throughout the organisation (Australian/New Zealand Standard 4360, 2004). For

example, the task identified may be as diverse as grinding metal samples; changing

the toner in a photocopier; transporting material from one area to another;

transferring biological samples into test tubes; decanting and mixing paints and

solvents; operating machinery such as cranes, hoists and fork lift trucks; undertaking

repair work inside confined spaces; undertaking cleaning work; spraying chemicals

such as pesticides. It is also necessary to consider future tasks or situations that

involve a change to the existing premises or process, or those which are non-routine.

2.3.2.3 Analysing Tasks

Once the task inventory is completed each activity must be analysed to prepare for

the identification of all hazards involved. In order to later analyse the risks associated

with the hazards, a manageable level of detail is required and this means that some

tasks must be broken down further into component elements. Each of these elements

is then examined in terms of its activities, use of plant and equipment, use of

substances and materials, processes, and the place where it is carried out. Following

are the elements that may be included in a task:

• Individual activities;

• Substances and materials;

• Plant, tools and equipment involved;

• Characteristics of the place where the task is carried out.

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The easiest method of breaking tasks down into elements is usually to consider how

the task is undertaken step by step (Australian/New Zealand Standard 4360, 2004).

For example, the task of diluting concentrated acid (e.g. hydrochloric acid) in a

laboratory involves:

• Preparing the work area;

• Putting on personal protective equipment (lab coat, glasses and gloves);

• Collecting the concentrated acid container;

• Pouring the acid;

• Labelling the container; and

• Clearing and cleaning up the work area.

2.3.2.4 Identifying the Hazards Involved

After breaking down the task into its elements, the next stage is to identify the

hazards involved. In undertaking the hazard identification task, there are many

different factors to consider - those related to specific hazards, individual tasks,

workplace conditions, particular people involved and unique circumstances.

2.3.2.5 Considering the People Factor

An important factor to consider is the people who may be exposed to risks from

hazards, and how any individual characteristics may impact on exposure. Gathering

this information at the hazard identification stage will assist with later risk

assessment efforts. In most cases, those affected will be the people involved in the

tasks. During hazard identification, try to take note of 'people issues' such as

(Australian/New Zealand Standard 4360, 2004):

• Any special characteristics which should be taken into account for example,

inexperience, chemical susceptibility and ergonomic issues (such as height or

prior injuries)

• Whether people other than operatives could be affected

• How these groups of people are affected by the circumstances surrounding

the task, such as normal operation, peak production, environmental factors,

maintenance activities and working alone.

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2.3.2.6 Aiding Hazard Identification

There are a number of activities that can be carried out to assist with identifying

hazards present in the workplace. These activities may be conducted in parallel with

other risk management functions and processes such as development of task

inventory and risk assessment activities. Some of those activities include:

• Undertaking a workplace walk-through;

• Analysing available information;

• Conducting workplace inspections; and

• Maintaining and using checklists.

Undertaking a workplace walk-through: Walking through the area which the

hazard identification has targeted is an essential information-gathering exercise even

if the team or individual involved is familiar with the task. Observing how work is

carried out will reveal valuable clues about the hazards involved. Sometimes it is not

a good idea to fully rely on the organisation's standard operating procedures for

details on how specific tasks are undertaken as workplace practices may vary greatly

from the international or national standard rules.

Analysing available information: Another important aid to identify hazards is to

check all available information. In the current context, this may assist in identifying

potential hazards from the types of plant, substances and work procedures at the

workplace. Amongst the key sources of information, which may assist in indicating

how hazards have arisen in the past, and are likely to happen again, are:

• Incident and first aid records;

• Plant maintenance and breakdown records (such as service books);

• Work systems and procedures documentation;

• Safety and health policies both general and specific;

• Employee training records;

• Operators' manuals and equipment instruction booklets, which often point out

safety "dos and don'ts'';

• Injury/incident data, workers compensation statistics and guidance material

from Workplace safety monitoring organisations such as WorkCover - NSW;

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• Australian standards which provide specifications for issues such as design,

manufacturing, inspection, testing, use and work methods.

While reading and analysing the information from these resources, take note of

hazards and conditions which may be relevant to the workplace. Developing a list of

potential hazards may prove valuable as a prompt in identifying hazards at the

workplace (Australian/New Zealand Standard 4360, 2004).

Conducting workplace inspections: One of the most important aids to hazard

identification is the workplace inspection. This may be conducted as part of, or

independent of, the workplace walk-through. Inspections can focus on specific tasks,

locations or hazards. Essentially, the inspection should be regarded as a fact-finding

mission to detect potential hazards. Before undertaking the inspection, it is vital that

those assigned to the task are fully briefed on employees’ roles. Activities undertaken

during the inspection may include:

• Taking notes;

• Interacting with employees;

• Observing work being done;

• Taking measurements (such as noise level readings); and

• Taking photos.

Maintaining and using checklists: Checklists are an invaluable aid in any safety

exercise (Australian/New Zealand Standard 4360, 2004). They assist in ensuring

that:

• Important issues are not overlooked;

• Consistency is achieved if the required activity is being undertaken by several

different people; and

• There is a formal record of efforts made.

To gain maximum benefit in hazards identification, any checklists used should be

specifically developed for the individual workplace. This will ensure that

circumstances unique to that workplace are taken into account. Examples of

checklists can be obtained from any Safety and Health web pages. These may be

used as a basis from which a customised checklist can be developed.

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2.3.2.7 Hazard Identification as Ongoing Process

Hazard identification does not end with the initial investigation. Hazard identification

should be regarded as an ongoing, integral part of workplace operations. In general,

the legal requirement is for hazard identification to be undertaken:

• Before and during the introduction of new work systems, plant and chemicals

to the workplace

• Before and during alterations or changes to the use or location of work

systems, plant and chemicals

• Where new information on hazards or control measures becomes available.

In order to fully comply with this requirement, a hazard monitoring system should be

put in place. This will form a part of the monitoring and review element of a safety

program.

2.3.2.8 Recording Hazard Identification Data

Once gathered, the hazard identification data and information must be recorded in a

risk register database so that it can be used for risk assessment activities and in

determining appropriate control measures. In practice, the same database may be

used to update hazard identification information, risk assessment information and

details of control measures to be implemented.

Review information: In considering likelihood, it is important to review the

information, which was gathered during the hazard identification stage. This may

include, for example:

• Hazard identification checklists (which will indicate the factors taken into

consideration);

• Hazard identification record database (which will provide valuable

information on circumstances surrounding the hazard together with

comments of the identification team or individual);

• Incident and first aid records (which should reveal trends or frequencies of

injury;

• Incident investigation reports;

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• Plant maintenance and breakdown records (such as service books);

• Work systems and procedures documentation;

• Safety and health policies both general and specific;

• Employee training records; and

• Operators’ manuals and equipment instruction booklets.

Other important sources of data include national incident, injury and workers

compensation statistics, which provide information on the numbers and frequencies

of accidents, related to type, activity and industry sector.

2.3.3 Undertaking Risk Assessment

As discussed earlier, risk is the potential outcome of a hazard. In other words, it is

the possibility that injury, illness, damage or loss will occur as a result of a hazard.

Since risk and safety are very closely related each other, there is a strong need for

evaluating risks, leading to the need for assessing the level of safety.

2.3.3.1 Risk Assessment

Risk assessment is the process of assessing all possible risks associated with each of

the hazards identified during the hazard identification process. There are a number of

different ways to assess risks. Some of the key points about assessing the risk in the

workplace are as follows (Australian/New Zealand Standard 4360, 2004).

• Assessment must cover all risks to the health and safety of employees;

• Assessment must cover risks to non-workers, such as sub-contractors and the

public, who may be affected by the employer’s actions;

• Prior to the introduction of new or changed work practices, substances or

plant, the employer must review the original assessment. A regular review is

advised as part of good management practice;

• Employers must carry out an assessment of first-aid requirements in their

workplace and ensure that appropriate equipment, facilities and trained

personnel are available and readily accessible in the workplace; and

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• Where groups of workers are especially at risk, they must be identified as part

of the assessment, e.g. young, inexperienced, or workers with a disability.

In assessing the risks, the following three essential elements (Figure 2.6) are generally considered. • The exposure of a hazard causing an accident;

• The probability or likelihood of the accident; and

• The potential accidental consequences.

Based on the estimation of these three elements the risks are calculated and ranked,

and priority is assigned for risk control through the use of the rating of risk rank.

Risks associated with an identified hazard need to be assessed in order to determine

how severe or dangerous they are. Assessing the risks allows employers to make

decisions as to what hazards or risks need to be controlled and to set priorities for

introducing controls. When assessing the risk any controls that are already in place

need to be taken into account. Two important laws of human nature should always be

part of the assessment (NT WorkSafe 2003, p.11). Firstly, never rely solely on

common sense, as it is much less common than is generally assumed. Secondly,

always rely on Sod’s Law. i.e. ‘if someone can do it, sooner or later someone will’.

1. Risks Exposure

Risk

Assessment 2. Likelihood / 3.Consequence Probability of Event of Event

Figure 2.6: Three Elements in Determination of Risk Assessment

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In order to undertake risk assessment, it is necessary to understand the nature of risk.

Risk assessment involves examining and evaluating the exposure of hazards, and the

likelihood and possible consequence (severity) of the potential outcomes of hazards.

Assessing risks can be carried out using a range of methodologies which are

available - from qualitative to semi-quantitative to quantitative approaches. Risks can

be quantified by determining the likelihood and consequence of a hazard against

known standards. The most common way of assessing risk by qualitative methods

includes methods using an employee’s experience and the information found on

experience and incident records. In this research, assessing the risk is approached by

quantitative methods. Risk is assessed using key measures of a hazard’s exposure,

the probability of an event occurring and its consequences.

2.3.3.2 Risk Assessment Matrix

A risk assessment matrix is a simple tool that can be used to assess a risk by

evaluating a hazard’s exposure, its likelihood of occurring and its potential

consequences. This enables the user to identify the appropriate response and

prioritise the implementation of controls. The process of risk assessment matrix

involves the following steps:

1. Measure the exposure of a hazard occurring;

2. Evaluate the likelihood of the hazard;

3. Estimate its potential consequences;

4. Quantify the risk of the hazard by combining 1, 2 and 3; and

5. Identify the risk of the hazard and the appropriate action required.

Exposure: The first step is to measure the exposure of the hazard. For example, how

many people are exposed to the hazard and for how long? This measure is required

when setting priorities for introducing controls. A typical example of measuring the

risk exposure with three descriptors ranging from hazard potential is shown in

Table 2.1.

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Table 2.1: Typical Measure of Risk Exposures

Exposure of Risk Description

High Exposure High hazard potentials in a small size group of people

Medium Exposure Medium hazard potentials in a medium size group of people

Low Exposure Low hazard potentials in a large size group of people

Likelihood: The next step is to determine the likelihood of the hazard. The method

of determining the likelihood that injury, illness, damages or loss will occur as a

result of hazards may vary according to the type of workplace and operations

involved. A basic system of evaluating likelihood is shown in Table 2.2, the measure

of likelihood is split into five descriptors ranging from events that are considered

'Very Likely' to hazards that would be considered 'Highly Unlikely'. It may be

determined that someone would be very likely to trip over raised paving slabs of a

frequently used path and 'Highly Unlikely' for someone to trip over a lifted floor tile

in a rarely used store room.

Table 2.2: Typical Measure of Likelihood

Descriptor Desc ription

Very likely It is expected to occur at some time in the near future

Likely Will probably occur in most circumstances

Possible Might occur at some time

Unlikely Could occur at some time

Highly unlikely May occur in exceptional circumstances

Consequences: The third step is to measure the potential consequences should a

hazard be realised, and its effect on exposed people. For each hazard identified, ask

the question ‘What if?’ In other words, the question is “what is the worst likely

outcome from hazard exposure?” As shown in Table 2.3, consequence has been split

into five descriptors varying from an outcome resulting in 'Negligible' injuries for the

most minor instances to 'Fatality' should one or more people be killed. The severity

of the injury may be rated as 'major injury' if the potential result is permanent

disability of the worker or a 'first aid injury' if the result of the injury at most would

be minor cuts and scratches.

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Table 2.3: Typical Measure of Consequences

Descriptor Description

Fatality Death

Major injury Extensive injuries, lost time injury >5 days , permanent disability (e.g. broken bones,

major strains)

Minor injury Medical treatment required, lost time injury from 1 – 5 days (e.g. minor strains)

First aid First aid treatment where medical treatment not required (e.g. minor cuts and burns)

Negligible Incident does not require medical treatment, property damage may have occurred

Measure of risk: The final step in assessing a hazards risk is to combine the

perceived likelihood and consequences determined above to identify the appropriate

action. For example, it is noticed that a storm has resulted in a power line coming

down across a footpath. The determination of the potential risk of such a hazard

would be a combination of the likelihood of a person being exposed, 'Likely' and the

potential consequences, 'Fatality'. By connecting 'Likely' and 'Fatality' on the matrix

shown in Table 2.4, it can be seen that this hazard is designated as an 'E' or 'Extreme'

risk. Immediate action is required to prevent the likelihood of a 'Fatality'. If the

hazard is identified as 'Extreme' and, as seen from the table, immediate action is

required, the appropriate Health and Safety Authority should be notified.

Table 2.4: A Typical Risks Assessment Matrix

Exposure

of Risk

High Exposure Medium Exposure Low Exposure

Likelihood (Probability of Event)

Consequences

of Event

Very Likely Likely Unlikely Highly unlikely

High Fatality Extreme Extreme High Medium

Medium Major injuries Extreme High Medium Medium

Minor injuries High Medium Medium Low

Low Negligible injuries Medium Medium Low Low

E (Extreme risk) - immediate action required; notify supervisor or appropriate Health and Safety

Authority as required;

H (High risk) - notify supervisor or Health and Safety rep immediately;

M (Moderate risk) - immediate action to minimise injury e.g. signs; supervisor remedial action

required with 5 working days; and

L (Low risk) - remedial action within 1 month, supervisor attention required.

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Risk assessment enables employers to plan, introduce and monitor measures for

ensuring that risks are adequately controlled. Events or situations that are assessed as

very likely with fatal consequences are the most serious (high risk). Those assessed

as highly unlikely with negligible injuries are the least serious (low risk). When risk-

control strategies are developed, employers should tackle anything with a high rating

first. Table 2.4 provides a typical risk matrix to assess the risk in accordance with the

level of risk exposure of an event, likelihood and consequence of the event.

2.3.3.3 Recording Results of Risk Assessment

It is most important that the conclusions reached about risks are documented and that

any supporting information on how these conclusions were made is included in

associated records. This is not only a legal requirement of the Occupational Health

and Safety Act 2004 but is also important for corporate knowledge and demonstrates

how a decision was achieved with regard to investigating a hazard.

Risk assessment records: Once the risk assessment process has been completed, the

results need to be recorded in a systematic manner. This means itemising the:

• Work sector, division or department involved;

• Name of the person heading up the risk assessment;

• Date on which the assessment was completed;

• Work zone or location of the hazard involved;

• Task, activity or work process involved;

• Hazard involved;

• People who may be exposed to risks from the hazard;

• Likelihood ranking of the risk (such as 'very likely');

• Severity ranking of the risk (such as 'fatality); and

• Risk rating assigned (the numerical value about priority such as 'extreme').

Acting on the risk assessment results: The risk ratings determined during risk

assessment enable decisions to be taken on the amount of effort to be expended in

controlling risks associated with particular hazards. However, any hazard that is

'highly likely' or 'certain/imminent' to cause harm needs to be attended to and the risk

reduced even if the severity is low. Those hazards identified as not adequately

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controlled can now be itemised in a prioritised list for action using the risk rating as a

guide to those which will require urgent attention (and possibly suspension of

operations), and those which can be listed for action sometime in the future.

2.3.3.4 Considering Current Controls

It is important that the effectiveness of any control measures already provided is

maintained and considered for further improvements. At the same time, it is

necessary to consider the possibility of current control measures not being used due

to issues such as:

• Lack of training or supervision;

• Failure to replace controls following cleaning, maintenance or repair work;

• Difficulty or awkwardness in using or working with controls; and

• Complexity of controls.

Once the likelihood and consequences of the potential hazard have been rated, it is

now possible to prioritise the risks based on these two criteria. Prioritising risk is the

final step in the risk assessment process.

2.3.3.5 Setting Times Limits for Action

Among many methods of dealing with actions to control risks, setting time limit

bands against the risk rating score is a common one. Time limit bands commonly

used include:

• L (Low) - must be attended to preferably within 1 month but issues such as

funding may make it more appropriate to rectify the hazard within up to

12 months.

• M (Moderate) - should be attended to within five working days and interim

controls put in place immediately.

• H (High) - risks should be attended to within one working day and interim

controls put in place immediately.

• E (Extreme) - risks must be attended to immediately. It is preferable that

activities are suspended until controls are in place.

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In setting these time scales (time limit bands), it should be remembered that the

control measures for risks associated with individual hazards vary enormously as far

as time, cost and other resources are concerned. It is essential for realistic time limits

to be set for the various items to be dealt with in the same way that other

management objectives are given deadlines. Once the risks associated with all of the

hazards identified have been assessed and control measures have been introduced,

the risk assessment exercise can be repeated to decide if the residual risk has been

reduced to trivial or adequately controlled levels. Continual assessment forms part of

the monitoring and review phase of risk management.

2.3.4 Risk Control or Elimination

Risk control is the process by which the risks associated with each of the hazards

present in the workplace are controlled. The process is executed using the priorities

(and any related time scales) determined during the risk assessment phase. The

primary aim of risk control is to eliminate the hazards leading to the risks, thereby

eliminating the risks. In situations where this is not possible, risk control seeks to

minimise risks by modifying or controlling the hazard and/or the associated work

systems (Australian/New Zealand Standard 4360, 2004).

2.3.4.1 Risk Control Involvement

Risk control provides a means by which risks can be systematically evaluated against

a set of control options (the hierarchy of controls) to determine the most effective

control method(s) for the risk(s) associated with each hazard. This process involves

analysing the data collected during the hazard identification and risk assessment

processes, and developing a strategic plan to control the risks identified. A form

called ‘Risk control schedule form’ assists in the allocation of tasks to relevant

people and the prioritisation of controls. The risk control process starts by

considering the highest ranked risks and working down to the least significant. Each

risk needs to be examined having regard to the 'hierarchy of controls'. This provides

a method of systematically evaluating each risk in order to determine firstly if the

causal hazard can be eliminated and otherwise, to find the most effective control

method for each risk.

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2.3.4.2 Hierarchy of Controls

In the event that an unacceptable risk to health and safety has been identified, control

needs to be introduced to reduce the risk to an acceptable level. There are a number

of ways of controlling risks in the workplace. These are known as the “Hierarchy of

Controls”. Placed in order of effectiveness they are as follows.

Eliminate the hazard: For example, remove trip hazards in a crowded corridor.

Dispose of unwanted chemicals.

Substitute with something of a lesser risk: For example, in manual handling, use

smaller packages. Use a less toxic chemical.

Isolate the hazard: For example, store chemicals in a locked enclosure. Use trolleys

to move heavy loads.

Personal protective equipment: For example, hearing and eye protection, hard hats,

gloves to be provided and worn.

Use administrative controls: For example, provide training and adequate

instruction on work practices. Provide adequate supervision. Ensure regular

maintenance of plant and equipment. Limit exposure time by implementing staff

rotation.

Back-up controls: Controls should be selected from as high up the list as is practical

for maximum effectiveness. In many cases, a combination of the above will be

necessary to reduce the level of risk. Back-up controls (such as personal protective

equipment and administrative controls) should only be used as a last resort or as a

support to other control measures. Worker involvement is essential to the decision-

making process for implementing risk control.

Control worst first: While the risk control process concentrates on controlling the

highest ranked risks first, this does not mean that lower priority risks, which can be

controlled quickly and easily, should not be controlled simultaneously. The best

available control measures should be put in place as soon as possible. In some cases

it may be necessary to put temporary controls in place until such time as the proper

controls can be instituted. Wherever there is a high risk and the control measures are

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not immediately available, temporary controls which reduce the risk(s) must be put

in place or the activity must cease until adequate controls are implemented.

Using the hierarchy of controls: The hierarchy of controls are developed by safety

regulators to assist employers in finding the most effective control measures for

hazards in their workplaces (NT WorkSafe 2003). When examined in greater detail,

the controls hierarchy may be divided into three levels, the second two levels

involving several elements:

• Level 1: Eliminate the hazard.

• Level 2: Minimise the risk.

o Substitute with a lesser hazard.

o Modify the work system or process.

o Isolate the hazard.

o Introduce engineering controls.

• Level 3: Institute back-up controls.

o Implement administrative controls and safe work practices.

o Require personal protective equipment to be used.

2.3.4.3 Sequence of Risk Control

A schedule should then be drawn up outlining the deadlines by which each control

must be implemented, and the people responsible. During the process of determining

appropriate control measures, and scheduling and implementing these controls,

records need to be kept.

Deciding on controls: The best control measure is determined by considering each

of the 'hierarchy of control' options starting at the top and working down. The higher

on the list the control we choose, the better the results should be. Unless we

completely eliminate the hazard, which is the first control option, we may need to

consider using more than one control simultaneously. Both elimination and

substitution control the hazard itself. They are, therefore, more effective in reducing

risk than controls which reduce exposure and which therefore do not reduce the

hazard itself (such as modification or isolation).

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Controlling exposure does not generally reduce the consequence, or severity (factor

of the risk), although it can reduce the likelihood of harm occurring. Another

limitation is that controls on exposure can be more easily removed or defeated.

Therefore, there will be a need to set up higher standards of supervision,

maintenance, checking, training and other administrative measures. Engineering

controls consider the question: 'Is it possible to use engineering controls such as

lockout procedures, process changes, presence-sensing systems, ventilation or

machine guarding to reduce the risk?' Back-up controls may take the form of

administrative controls or provision of personal protective equipment. Administrative

controls involve the use of management systems to minimise risks and promote

workplace safety. At any workplace, the primary administrative control, which

should be in place at all times, is the use of safe work practices. This should include

the use of written procedures to indicate:

• How tasks are to be undertaken;

• Who is permitted in the work area;

• What the requirements for operating different types of equipment are;

• Operator competencies; and

• Any training and supervision needed.

Other examples of administrative controls, which may be used, include the

following:

• Providing worker rotation so that the same workers are not exposed all the

time;

• Rescheduling operations to times when there are fewer workers around;

• Providing one-way traffic flow to minimise traffic hazards;

• Instituting purchasing controls where a hazard has been eliminated to ensure

that, for example, a solvent-based adhesive is not purchased by someone in

the organisation who is unaware of the decision to use only the water-based

alternative; and

• Providing adequate information, instruction, training and supervision to

ensure that employees undertake their work safely.

Personal protective equipment (PPE): This involves some form of equipment

being worn by workers who may be exposed to hazards, to shield their bodies from

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harm. For the most part, PPE shall not be used as a primary means of protection, but

only as a back-up to support other control measures.

Documenting risk control: The risk control process needs to be fully documented

and these records kept with other relevant risk management records. Controls can be

documented on the Risk Management Matrix, as part of a Risk Control Record Form.

2.3.4.4 Undertaking Monitoring and Review

Monitoring and review is the final stage of the process. This stage of the process

keeps risk management current and effective, as new hazards and those overlooked

in the original process are identified and controlled. Monitoring and review involves:

• The systematic re-implementation of the original steps of:

o Hazard identification

o Risk assessment

o Risk control

This is to ensure that the process was undertaken properly and that, in

hindsight, the conclusions were correct.

• Ongoing monitoring of existing risk control measures to assess their

effectiveness in light of changes and fluctuations in the workplace

• Collection of data on any new hazards which may have arisen and the

formulation of new control measures

• Review of the risk management process to ensure that all new hazards

identified are controlled.

Aids to monitoring and review: In repeating the original elements of our safety

program, other related activities need to be undertaken periodically as part of the

monitoring and review system. These include:

• Scheduled inspections;

• Ongoing measurement and testing;

• Workplace monitoring where necessary (for hazards such as noise and air

contaminants); and

• Periodic incident analysis.

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In overall, the aims of a risk assessment determine the types of output required and

the approach taken. A range of methodologies are available from qualitative to semi-

quantitative to quantitative approaches. Risk assessments can be used for corporate

overviews, to prioritise risks and screen options to define management focus, or

applied to specific events or planned tasks. The context description and aims of the

risk assessment also help determine what structure is required for the risk

assessment, and the nature and levels of expertise required to identify and to describe

key risk events.

2.4 Safety Risk Potentials in Railways

Safety is one of the critical aspects in railways, given that it deals with the safety of

large volumes of people across a huge transportation infrastructure, compared to

safety at workplaces which deals mainly with employees. The Transport sector is

expected to deliver services to their customers at a high level of safety. Although the

Rail sector has been reasonably good at doing this for a long time, many thousands

of people (the public, passengers and employees) are injured globally in railway

accidents each year (United Nations 2000). The following consequences result in

these railway accidents:

• Several billions of dollars are paid in medical costs and disability payments;

• Medical insurance premiums are increased to meet the rising costs;

• Capacity of productivity is decreased;

• Loss of lives and human suffering;

• Inconvenience caused to injured people, to others and to the environment.

Railway occurrences (accidents and incidents) don’t just happen, nor are occurrences

completely accidental. There may be many hidden factors, including the failure of

one or more safety components of the railway system, which contribute to railway

occurrences. Identifying, prioritising and targeting the hazard potentials which cause

railway occurrences, and developing mitigation initiatives and controls on these

hazard potentials can prevent such occurrences. Nevertheless, we find ourselves now

in a world where the opening up of the commercial availability of railways and the

search for an optimum level of safety, taking economic and organisational

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constraints into account, is a priority target at the very heart of development strategy

on all continents.

Safety of passengers, customers, the public, contractors and staff is an absolute pre-

requisite for safety management development in railways. Emphasis has been placed

on complying with statutory and Railway Inspectorate requirements, promulgating

Rules and Procedures, the training of staff, and enforcing discipline and compliance.

This approach has been appropriate and successful in establishing a good safety

performance from the beginning of railway operations. There is doubt as to whether

continuation of this management approach is adequate in coping with the increasing

complexity of railway operations, since the following issues were noted:

• The tendency for safety performance to depend on the expertise of key senior

operations and management personnel;

• Lack of understanding on the part lower level staff have to play in ensuring

the safe operation of the railway;

• The concept of safety is not sufficiently integrated into daily work practices;

• Inquiries into serious railway accidents worldwide highlighted the following

desired features in modern safety management:

o Adopting a formal and systematic approach to managing safety; and

o Conducting safety audits to provide assurance in safety management

performance

• A comprehensive program of risk management is crucial to safety

management.

The Railway Safety Act (RSA, 1989) and the amendments which came into force

later (RSA, 1999) redefined roles by implicitly placing crossing safety

responsibilities on the railways and the road authorities (Railway Safety Transport

Canada 2000, p.1). This policy reflects the objectives of Section 3 of the RSA, which

includes:

• Promote and provide for the safety of the public and personnel, and the

protection of property and the environment in the operation of railways;

• Encourage the collaboration and participation of interested parties in

improving railway safety;

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• Recognise the responsibility of railway companies in ensuring the safety of

their operations; and

• Facilitate a modern, flexible and efficient regulatory scheme that will ensure

the continuing enhancement of railway safety.

2.4.1 Priority Issues Id entified in Rail Safety

This section describes most of the priority areas identified in rail safety issues. They

are not placed in order of priority. They are divided into two major groups (Fig 2.7)

as follows (ETSC 1999):

• System based safety issues; and

• People based safety issues.

1. System Based Safety Issues

• Signal Passed at Danger (SPAD) • Automatic Train Protection (ATP) • Lack of Co-operation at Global Level • Comprehensive Rail Safety Information • Safe Team Work in Various Railway

Operations • Privatisation of Railways • Formal Safety Operational Recognition • Independent Bodies for Accident

Investigations

2. People Based Safety Issues

• Driver Alertness • Drugs and Alcohol • Job Training • Effective Communication • Train Boarding and Alighting • Employees Working on or about the

Track • Dangerous Goods • Level Crossings / Track Invaders

Priority Rail Safety Issues

Figure 2.7: Two Major Groups Identified in Rail Safety Issues

The first group describes the major issues in the system of rail safety processes and

procedures, and the second group explains the major issues due to the involvement of

the people who interface with the rail operations. However, these two groups interact

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in some ways. For example, although the event of Signal Passed at Danger (SPAD)

occurs mostly due to system-based problems, sometimes it may be due to people-

based errors. The two groups are discussed in greater detail below.

2.4.1.1 System Based Safety Issues

Signal passed at danger (SPAD): A signal passed at danger is a precursor safety

occurrence - an event which could, under specific circumstances, lead to an accident

such as a collision between trains. The actual risk of collision following a SPAD

depends on many factors including whether the signal is equipped with engineering

defences which automatically stop a train once it has passed a red signal, whether the

train travelled into another section of track and whether that section was occupied.

Train collisions and derailments account for almost all the multiple-fatality and high-

profile accidents, and all countries have a sombre roll-call of places where serious

railway accidents have occurred (ETSC 1999, p.7). Train accidents have a wide

variety of causes, including vehicle or track defects, defects in the signalling systems,

and errors by operating staff. Accidents due to errors by signalling staff in normal

operation are now rare, because modern signalling systems have automatic protection

against such errors. However, accidents due to errors by drivers, such as passing

signals at danger are more common, because it has been more difficult to develop

automatic protection against these errors. Such errors are never deliberate, and they

are very infrequent for each individual driver, but for systems as a whole they are a

persistent problem. The causes of SPAD can be classified as follows:

• Signal not seen due to bad visibility

• Misjudging of which signal applies to the train in question

• Misunderstanding or disregard of the signal

• Misjudging the effectiveness of the brakes under particular circumstances

like driving trains on a wet day

• Over-speeding in relation to braking performance and warning signal

distance

• Broken driving sequence procedure.

Automatic train protection (ATP): ATP is speed and distance supervision,

intervening (usually deploying emergency brake, as a last measure) when the driver

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of a train omits to react on optical signals given from the wayside system. ATP is

given permitted speed and location information from the track via encoded radio.

With the development of modern processors, it has become possible to protect

against drivers' errors. ATP systems continually calculate the maximum safe speed of

a train in the light of current track and signal conditions, compare the actual speed

with the maximum, and apply the brakes automatically if the train is going too fast.

However, the main problem about current ATP systems is that, if they are installed

as an overlay on the existing trains and signalling systems, they have high costs in

relation to the relatively small number of casualties avoided. Therefore different

countries have different policies towards ATP. Many countries have installed it;

some are in the process of installing it, and some have decided against it, except in

special circumstances. It is less costly to install ATP on new trains and lines than on

existing ones. In the longer term, new train control systems can have ATP built-in at

no extra cost. It is desirable to make new systems interoperable.

Lack of co-operation at global level: Since railway operation and associated safety

issues have been primarily a domestic matter, each country has developed its own

procedures for railway safety regulation, and for investigating and recording railway

accidents. There has been less international co-operation in rail safety than in other

modes: aviation and maritime transport are more international by their nature, and

road safety is recognised to be a common issue in all countries. One consequence is a

lack of reliable and comparable global information on rail safety that in turn makes it

difficult to quantify the key railway safety problems at a global level and difficult for

the different states to learn from the successes and failures of each other.

Availability of comprehensive information on rail safety: Railways are receiving

increasing attention at the global level, because they are a major asset and they offer

the prospect of meeting transport needs with less environmental damage than roads.

The safety record of railways has been improving over the past decade. However, in

order to improve the safety level, a country cannot develop its national policies for

rail without actively including safety. The major current problem is the lack of

comprehensive rail safety information at the global level on which to base safety

policy. Safety representatives generally take rail safety seriously: they investigate

accidents and record data domestically, but there is no effective mechanism by which

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the results and findings of those investigations reach the global level: indeed, there is

a lack of central knowledge of what the safety representatives actually do.

Safe team work between various railway operations: Safe railway operation

requires very close co-ordination between train control, crew operation and station

operation. The main problems are due to confusion about the location of safety

responsibilities, and that some newcomers to the industry might be inexperienced in

railway safety. The general approach when separating railway activities has been to

allocate general responsibility for the safe operation of railways to the track

authorities, or infrastructure controllers. For example, the infrastructure controllers

will not only ensure that their own track and signalling systems are safe, but are also

often required to check the safety competence of any train operator who wishes to

use their systems. The infrastructure controllers are also in turn responsible to the

government or railway inspectorate for carrying out these functions.

Privatisation of railways: Privatisation of railways sometimes creates a fear that

private operators will take greater risks than public operators in order to enhance

their profits, and put commercial considerations ahead of safety. Given the limited

extent of rail privatisation, there is little evidence one way or the other whether this

fear is justified. Moreover, the argument can also go the other way, because a good

safety reputation is a commercial asset.

Formal safety operational recognition: As a result of railway fragmentation, safety

operational recognition requires more formal safety processes than in the past. The

most important formal process is for all railway operators to generate individual

documents for reviewing of their safety responsibilities. These documents, as

outcomes of this process, are labelled 'Safety cases'. The aims of such documents are

to:

• Give confidence that the operator has the ability, commitment and resources

to assess and effectively control risks; and

• Provide a document against which it is possible to check that the accepted

risk control measures and safety systems have been properly put into place

and operate in the way in which they are intended.

Safety cases or comparable documents should include:

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• The operator’s safety policy;

• An assessment of the risks generated by the activity;

• A description of the SMS; and

• A basis for safety auditing.

There are also some other ways in which rail fragmentation requires more formality

in safety management. For example, with a single national operator, driver training

and certification of competence could be carried out internally. That is no longer

possible, because staff may move from one company to another, and they now

require formal documents which prove their competence both to their new employer,

and to the infrastructure controller.

Independent bodies for accident investigations: Some countries now have

independent railway accident investigation bodies, whereas others do not. Not all the

new railway operators will be in a position to carry out high quality accident

investigations, so independent bodies will be more needed in the future.

2.4.1.2 People Based Safety Issues

Driver alertness: Lack of driver alertness is closely related to the continuing

problem of errors by drivers. The pressure for greater efficiency in the utilisation of

staff is tending to lead to fewer and longer work duty periods, and to the use of

single-operator shifts. There is little evidence so far of the impact on risk; medical

and psychological research suggests that some shift patterns are better than others.

The results of such research should be applied when designing new working patterns.

Ergonomic principles should be applied to the design of drivers' cabs. Medical and

psychological assessments are also seen as important in the selection of drivers, in

monitoring performance, and after incidents and accidents.

Drugs and alcohol: Alcohol abuse is recognised to be a problem in parts of the rail

industry. Whenever possible, it is desirable that drivers sign on for duty in the

presence of a supervisor trained to detect signs of alcohol consumption. However,

this is not always possible, especially where drivers sign on in remote locations. If

necessary, breath tests may then be used to measure blood alcohol levels.

Supervisors should also be trained in the detection of drug use, and employees

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should be provided with a list of all types of prescribed drugs that may impair

performance.

Effective communication: The history of railways contains many accidents and

fatalities that were caused by errors in communication. Communication errors take

many forms, including the misunderstanding of oral messages and misinterpretation

of written instructions, especially during abnormal or emergency working. These in

turn have many causes, such as regional variations in the use of language, poor voice

quality in radio messages, and lack of clear standards in the formulation of messages.

The issue of communication has surfaced again with the increasing use of mobile

phones within the industry. In Sweden mobile phones are used extensively, and all

communication is recorded. In Italy mobile phones are used, but only when a train is

stationary. In Germany, Australia, the UK and Ireland mobile phones are not used for

operational communications, but these countries have secure radio systems in which

safety messages are received only by the person to whom they are sent.

Job training: Training of safety-critical staff is becoming increasingly important.

Because of the long-term trend towards single-driver and single-operator trains, there

is less opportunity for knowledge transfer on the job. Multi-media train centres and

driving simulators are recommended. Staff should be advised of new safety

recommendations and the results of accident investigations. Increasing privatisation

makes it necessary to have a system of recognised transferable competencies backed

by law. Increasing cross-border operation means that train crews need an increasing

knowledge of more than their own territory operating systems. There is a need for

harmonisation in between the cross-border operating systems.

Train boarding and alighting: The severity of this problem varies from country to

country. In the UK, these accidents account for the majority of passenger fatalities

(ETSC 1999, p.8). There are still many vehicles in use in Europe with passenger

operated doors, which can be opened while the train is moving. This can lead to falls

from trains and to unwise attempts by passengers to attempt to board or alight from

moving trains. As in Australia, the trend now is towards trains with automatic doors

which can be opened during normal service only when released by the train crew,

and only when the train is stationary. However, it should be noted that automatic

doors do not remove all risk, and serious accidents involving automatic doors (such

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as passengers caught in doors and dragged) still occur. Sometimes the train crew

cannot see passenger boarding and alighting activities on platforms with a large

curvature. Different states and countries have different traditions about platform

heights. Some have heights that enable passengers to board trains on one level;

others have low platforms from which passengers have to climb into trains.

Increasing interstate train travel may require more harmonisation in this area.

Employees working on or about the track: Railway operation and maintenance

requires several groups of staff to work on or about the track: these include track,

overhead line, and signal maintenance staff, and shunters or couplers. This type of

railway work has long been recognised as a relatively high-risk occupation, and

deaths among such staff still regularly occurs in almost all countries. The key to

reducing such accidents is careful planning and management of these activities.

Wherever possible the requirement for staff to be on the track should be eliminated:

examples are the increasing use of automatic couplers, which reduces the need for

shunters on the track, and the use of radio communications, which reduces the need

both for drivers to use line-side telephones and for staff to maintain them. Track

maintenance work will be separated from the running of trains, and increasingly

sophisticated planning will allow this with minimum disruption to services. Where

staff is required to be on the track when the railway is operating, good safety systems

are needed: proper lookouts, warning procedures, and personal protective equipment.

Railway maintenance is increasingly being carried out by contractors rather than by

railway staff. This places additional responsibilities on the client to ensure the

contractors are familiar with all railway safety requirements.

Dangerous goods: Railways are a relatively safe mode of transport for dangerous

goods, and are significant carriers of them. Their main disadvantage is that for

historical reasons railways tend to pass through the centres of towns and cities where

there are populations nearby, whereas the newer motorways tend to go round the

outside of towns. Communication and information management are key aspects of

the safe carriage of dangerous goods, especially in relation to the contents of vehicles

and containers. However, loading and unloading of dangerous goods is generally

more dangerous than the actual movement. Dangerous working conditions often

exist, such as dirty or slippery conditions for staff who have to climb on and off tank

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vehicles. Poor repair of rail tracks can also cause problems. Staff training, especially

in dealing with emergencies, and personal protective equipment are important.

Track invaders: Many accidents happen at boundaries with other systems: suicides,

trespassers and animals on track invade the railway system for their own individual

purposes. To avoid those accidents happening, the railway territory will be protected

from public activities by building secure fences.

Level crossings: Almost all railway systems have large numbers of level crossings,

especially those in flat terrain. The vast majority of casualties at level crossings are

due to road users: motor vehicle occupants, cyclists and pedestrians. Many such

accidents are due to unwise actions by road users; it is not clear whether road users

take more risks at level crossings than at other road intersections, or whether level

crossings are more hazardous simply in comparison to other railway risks. Most

countries have statutory or non-statutory rules for the application and operation of

level crossings. Such rules cover the type of crossing that is to be used for specified

road and rail traffic levels, the maximum permitted train speeds for the different

types of crossing, the protective equipment required, video surveillance, road layouts

and gradients, and the warning sequences for road users. However, each country's

rules have developed separately, and are different from each other. The long-term

trend has been away from railway-controlled crossings towards automatic operation:

these put the responsibility for safety primarily on the road user. They reduce delays

and costs. Another solution is to replace level crossings with bridges or underpasses.

Several countries, including Sweden, Italy and the Netherlands have rolling long-

term programs for this. The priorities for these programs are railway lines with

relatively high speeds, lines where increases in speeds are planned, lines in urban

areas, lines on which dangerous goods are carried, and locations with poor visibility.

New high-speed lines are always built without level crossings (ETSC 1999, p.10).

However, level crossings are so numerous, with many on lightly-used roads and

railways, that there is no prospect of eliminating them entirely.

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2.4.2 Challenges of Safety Faced in Rail Sector

Safety has always been seen as a transverse subject with no one area or discipline

able to claim that they have a greater right to be the safety expert than any other.

Whilst this still holds largely true, the challenges facing the railway today requires

that the focus on safety management and the systems employed to demonstrate a

sound attitude towards safety take on an entirely different position. The Rail sector

recognises this as safety continues to play an important role for passengers, the

public, rail workers, rolling stocks and infrastructures. It has been engaged to support

this work and to be in place to concentrate on the challenges that liberalisation and

interoperability will bring to them.

Political Influences: It will be especially important to the Rail sector that political

decisions taken in respect to safety and interoperability remain compatible with the

continued competitiveness of rail transport, an issue that is important to rail

companies. The Rail sector prides itself on its ability to draw together members from

around the globe and enable them to work together on projects of strategic

importance through world-wide cooperation. Safety is a core theme traversing

practically all of these international co-operation works and projects. The Rail sector

has a responsibility to assure, as it brings together new interaction opportunities

which can contribute to developing the overall safety culture worldwide. Through

this exercise, development will be publicised so that we can collectively ensure we

maintain and indeed strengthen the overall cohesion of the railway system. It is

above all through this level of cohesive co-operation that we will collectively retain

our premier position in relation to other modes of transport and safety.

Third Party Operators: United Nations (2005, p.4) stated that the control of risk is

something of vital importance to the Rail sector. Third party risk (brought about by

issues not within the control of the Rail sector) is one of the biggest contributors to

the overall level of safety on the rail network. Only a minority of rail accident

fatalities involve passengers travelling in trains. Data analysis suggests that injury to

a third party is four times more likely than to a passenger travelling in a train.

Overall, the major area of risk to the industry comes from this area and is largely as a

result of incidents on level crossings and trespass.

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Rail Workforce: As with most challenges, the looming shortfall in the rail labour

workforce will place pressure on the capacity of the Australian rail industry (Sochon

2004, p.3). This has genuine implications for rail safety. For example, fewer workers

will mean reduced services and productivity where technology has not been seen as a

viable alternative. This is true of the situation of train drivers and guards, given that

driverless trains in virtually all operating environments are unlikely for the

foreseeable future. With reduced capacity in numbers of safety workers comes

increased pressure on existing safety workers. This then leads to the increased

likelihood of pressure and fatigue-related accidents and incidents, notwithstanding

current excellent initiatives to improve fatigue management in the industry.

Lack of Training: Furthermore, the pressures on productivity from inadequate

staffing levels impact on the ability of the industry to undertake all but the basic

needs of training. The industry is currently focussing on the important area of

“human factors” training as a way of improving work safety. This kind of new and

important safety training is likely to suffer when workforce levels are insufficient.

Interestingly, the shortages in staff will in turn lead to a worsening perception of the

industry and this may adversely affect recruitment. Finally, the inadequacy of

training deriving from shortages in staff can serve to undermine the very safety

culture of organisations, as staff perceive that safety training for all but the very

essential areas is given low priority.

Travel Growth: Despite the attempts of some governments to discourage travel as

one way of easing the congestion of roads, rail and air space, it can be seen that there

will be an annual growth of several percent in all modes. This is partly a result of the

globalisation of business, generating much more transport to bring goods from the

cheap labour economies to the high consumption societies of the developed world.

Globalisation creates more business travel, as international companies try to keep

control over their empires; travel which expands despite information technology

enabling the message to travel rather than the person. But it is travel for pleasure

which is driving the market; foreign holidays, a moneyed class of early retirees with

time on their hands and a dispersion of families across countries. The challenge is to

manage this growth with a commensurate increase in safety per kilometre travelled.

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Advanced Technologies: As a response to this, railways are expanding rather than

cutting lines (Hale 2000). The high-speed train network is spanning Europe and

forcing technical harmonisation as never before. Interoperability of trains on the

underlying intercity networks is becoming increasingly vital. New forms of rail (or

rail-like) transport are being introduced, from the Maglev to the light rail hybrids

with trams (Nash 2007). Technologies such as tunnelling are being extended to new

applications, such as the tunnels in the Netherlands to free up the above ground space

or to reduce nuisance noise, and to new challenges, such as the Channel Tunnel. GPS

and other positioning techniques, together with better en route communication, are

changing traffic control techniques radically.

Globalisation: New technology always brings with it new safety challenges.

Globalisation means that national markets, such as those for railways, are being

opened up to foreign ownership, which brings with it new ideas of how to manage,

including how to manage safety. Competition also is increasing, bringing other cold

winds of change into the newly privatised railway companies. The response in many

industries has been a major reorganisation of company boundaries and the

outsourcing of much peripheral work, while core businesses seek to grow by

acquiring their direct rivals, whilst at the same time splitting their own activities into

(local) business units. Slogans such as "think global, act local" summarise this new

concern for explicit competitive management. With new boundaries come new needs

to define how safety can continue to be achieved in this rapidly changing world.

2.5 Rail Safety Management System

As discussed earlier, safety is central to all rail operations across many functional

areas within the railway - employees, passengers, customers and stakeholders. It is

therefore associated with central principles applied to all rail operations. However,

there are only two central principles appearing a number of times (Elms 2001,

p.296). The first is the need for integration (i.e. integration of data, applications,

organisational structures for the different aspects of a rail safety system) and for

safety to be integrated into the mainstream of the business and not held to one side in

a reactive mode. The second is the need for a trade-off between cost and benefit, as

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an underlying management practice. Both principles support not only good safety,

but also good business.

There is always a growing need to operate safely as accidents are frequent and their

consequences often grave. Wu (2006, p.1) stated that the past years have witnessed

an upsurge of accidents in which management and/or system factors played a major

causative role. Despite attention often being centred on the immediate causes of an

accident, many root causes are in fact attributable to management and/or system

factors. These factors unfortunately are more potent and can create numerous

opportunities for accidents. As a result, safety professionals have explored them

intensively. This area was identified as an area warranting the closest attention,

notwithstanding the fact that safety performance on the railway had been

satisfactory. With the system refined over time, improvement has been achieved, by

carrying out external benchmarking and external expert reviews. Innovative SMS,

subsystems and processes have evolved over many years. The evolution is expected

to continue in the future and so does the need for further research on SMS across all

operations.

2.5.1 Rail SMS as a Central System to All Rail Operations

The fundamental function of systems supporting the safety of railway operations is

ensuring that basic safety actions, such as stopping services in the event of an

incident and securing against the danger, are effective. It is very important to prevent

accidents and near misses; to raise safety and minimise transport disruptions, leading

to more reliable transport services. Rail Safety Management means a holistic,

systematic and optimal way of managing and controlling risks associated with rail

transport services to achieve desired safe outcomes in a sustainable way. As a result

of increasing the adoption of such systems, the global railway industry has become

reasonably safe in recent years. However, at this time the number of passengers is

rising at an unprecedented rate, freight traffic has grown and is set to expand even

further, and performance is improving. All this bears out what the Rail sector has

always known - that high standards of performance and safety are inextricably

linked. It provides what passengers and customers expect while creating the essential

condition for growth in the traffic (Rail Safety and Standards Board 2006). As the

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authority for maintaining safety, the Rail sector needs to assure itself and community

(public, passengers and employees) that the safety risks are being managed to levels

that are “As Low As Reasonably Practicable” (ALARP).

Safety is all around us and we need to strive to establish common management

practices that will ensure that collectively the Rail sector is facing in the same

direction. Based on a comprehensive review of its safety management using modern

principles and practices, a risk-based proactive SMS is identified as the central

system to all rail operations and is depicted in Figure 2.8 (Samaranayake, Matawie &

Rajayogan 2011, p.2). The system has been refined over time, based on experience,

and its quality and practicability have been benchmarked internationally as class-

leading (Wu 2006). This improvement has been achieved through the adoption of a

safety culture in individual rail operations. Many innovative safety management

subsystems and processes have been developed in this way and proven to be

effective through implementation. This research work provides partial assistance to

the rail industry in order to enhance SMS in their operations.

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Managing

People

Communication

Risk and Accident

Management

Maintenance

System

Development

and Implement of Safety Policy

Human Factors

Management

Operational

System

Design and Technology

RAIL SAFETY MANAGEMENT

SYSTEM

• Occurrence reporting and

recording, safety data collection • Safety performance analysis • Periodical Safety reports,

Safety plans and Safety targets • Risk Assessment processes • Risk Control Strategies • Occurrence Management • Occurrence Investigation • Corrective Action Procedures

• Safe design of rollingstocks • Safe design of infrastructure • Introducing safer technologies

Rollingstocks • Locomotives • Wagons • Track machines

Infrastructures • Tracks • Overhead track

equipment • Signals • Bridges • Level crossings

• Frequent safety

meeting between management and employees • Discussions on safety issues and

problems • Analysis and reports on safety

performance indicators • Publications of

periodical safety reports

Passengers • Train accidents • Health & safety • Security • Comfort journey

Public • Trespass • Suicide • Vandalism • Graffiti • Level crossing

road users

Railway Employees • Health & safety • Security • Safety culture • Training

• Railway Safety Policy Statement • Safety Organisation • Authorities, Responsibilities and Accountabilities • Employee and Representative

involvement • Safety Plan and Objectives • Compliance with legal requirements • Document and data control • Safety Change Management • Safety Performance Monitoring • Safety Audits • Safety Management System Review

• Human

Safety Standards • Safety

Critical Work

• Station

operations • Depot

operations • Signalling

operations

Figure 2.8: Rail Safety Management System as a Central System to All Rail Operations

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2.5.2 Development and Management of Rail Safety

Safety rules and standards, such as operating rules, signalling rules, requirements on

staff and technical requirements applicable to rolling stock, have been devised both

nationally and internationally. Under the regulations currently in force, a variety of

bodies deal with safety. These national safety rules, which are often based on

national technical standards, should gradually be replaced by rules based on common

international standards, established by technical specifications for interoperability.

The new national rules should be in line with current legislations and facilitate

migration towards a common approach to railway safety. In this connection, the Rail

sector ensures that:

• Railway safety is generally maintained and continuously improved, taking

into consideration the development of current legislations;

• Safety rules are laid down, applied and enforced in an open and non-

discriminatory manner;

• Responsibility for the safe operation of the railway system and the control of

risks associated with it is borne by the infrastructure managers and railway

undertakings;

• Information is collected on common safety indicators through annual reports

in order to assess the achievement of the common safety targets and monitor

the general development of railway safety.

In order to coordinate the different rules, a distinction needs to be drawn between:

• Infrastructure managers, who are bodies or companies responsible in

particular for establishing, building and maintaining infrastructure and safety;

• Railway undertakings, which are private sector service providers and

government agencies engaged in the supply of goods and/or passenger

transport services by rail.

2.5.3 Key Components of SMS Managed by Rail Sectors

The railway is committed to maintaining a high degree of safety awareness and

continuously employing management systems to strive for continuous improvement

in safety performance. A risk-based approach is generally adopted for managing

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safety internally by Rail sectors. The SMS provides a workable framework for

managing safety in a systematic, proactive and consistent manner, so that the Safety

Policy can be effectively implemented. It allows the railway to manage safety

systematically, similar to how other critical aspects of the business are managed, and

reduces the need for “safety experts” as safety management then becomes line

management’s responsibility. Most importantly, all staff involved can discuss safety

using the same language. Wu (2006, p.3) stated that the Rail SMS comprises the

following nine key components:

• Safety Policy

• Safety Tasks

• Safety Management Process

• Safety Responsibility Statements

• Safety Audit System

• Risk Control System

• Safety Critical Items

• Safety Committees

• Staff Consultation.

Safety Policy: The Safety Policy sets out the high level requirement for managing

safety and health risks. It declares that the safety of railway customers, the public,

contractors and employees is an absolute pre-requisite. The organisation is

committed to maintaining a climate of safety awareness and employing management

systems to assure corporate safety goals for continuous improvement in safety

performance in all aspects of the business. The policy also stipulates that safety

demands active involvement by all. Safety management is the line responsibility of

senior management staff. To maintain the climate of safety awareness, senior

management is committed to the following missions (Leung 2002, p.1):

• Setting high standards which consistently meet legal requirements;

• Giving specific safety responsibilities to individual;

• Training up staff and manage contractors to ensure safety in their activities;

• Maintaining safety communication channels at all levels;

• Employing management systems that will reduce risks to as low as

reasonably practicable;

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• Measuring safety performance by identifying appropriate indicators;

• Using internationally recognised modern practices and processes; and

• Providing necessary funding and resources.

Safety Tasks: Fifteen Safety Tasks have been identified as most important and

relevant for managing safety in the Rail sector in order to clearly define the scope of

rail safety management (Yiu 2004). Each Safety Task has an objective to be

achieved, supported by a number of Safety Modules that provide the standards to

meet. The fifteen Safety Tasks identified are as follows:

Task 1: Safety Information

Task 2: Safe Systems of Work

Task 3: Asset, Design and Project Management

Task 4: Protective Equipment

Task 5: Fire

Task 6: Human Resources

Task 7: Communication on Safety Matters

Task 8: Contractors and Visitors

Task 9: Emergency Preparedness and Response

Task 10: Accident Reporting and Investigation

Task 11: Safety Inspections

Task 12: Safety Performance Monitoring

Task 13: Funding for Safety

Task 14: Review and Audit

Task 15: Security

Safety Management Process: Having identified the Safety Tasks to be performed

and the standards to be met, middle managers need to manage the safety tasks using

a familiar management process similar to managing any other important aspects of

the business. This Safety Management Process need to be in alignment with the

guidance outlined in current national Health and Safety Acts and Regulations.

Successful safety management system comprises the following functions (Wu 2006):

• Policy: Within the context of a department or section, this includes a structure

of guidelines, procedures, and standards on safety. It should meet legal

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requirements and provide a framework for controlling risks to as low as

reasonably practicable.

• Organising: This involves distinguishing the roles of line management and

support staff, and establishing individual safety responsibilities.

• Planning: This includes setting performance targets, allocating priorities for

implementing safety initiatives, and allocating funds for safety items.

• Implementing: This comprises leading staff to implement safety initiatives,

communicating the requirements to staff, obtaining feedback, providing

training, generating safety awareness, etc.

• Monitoring: This includes safety inspections, performance monitoring, and

investigations of undesired events.

• Review: This involves a broader review of the SMS of a department, section,

or operation. Formal, independent safety reviews are also conducted.

• Audit: This involves assessment and evaluation of the adequacy,

effectiveness and conformance to a set of laid down procedures and standards

in a SMS.

Safety Responsibility Statements: The SMS also includes a system of Safety

Responsibility Statements (SRS), which sets out in writing the safety responsibilities

and accountabilities of each post, for supervisory grades and above. Individual staff

members are required to understand and discharge the responsibilities stated in their

own SRS. These SRSs are being used in human resource functions such as

recruitment, appraisal, and promotion. Staff members who are not provided with

SRS will be provided with a Safety Responsibility Card, which gives simplified

guidelines on their safety responsibilities.

Safety Audit System: The purposes of safety audits are to provide assurance on the

compliance and effectiveness of safety management, assist middle management in

identifying opportunities for improving safety performance, identifying new hazards

and raising safety awareness (Wu 2006). In general, there are four types of

independent safety audits conducted in the railway, including:

• System audit

• Activity audit

• Contractor audit and

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• Safety technical audit.

Risk Control System: The Rail sector is required to operate on prudent commercial

principles. To support this, a risk-based approach to managing safety has been

established which includes a systematic and proactive process for identifying

hazards, registering them, estimating the associated risks, establishing standards of

acceptability and tolerability, evaluating the risks, identifying and prioritising

mitigation measures, and tracking the hazards and mitigation measures. A formal risk

control process and organisation have been set up. Hazards are ranked according to a

Risk Matrix based on their expected frequency and severity. An interactive database,

(such as “Risk Register System” or "Hazard Register System"), will be in place to

facilitate risk control and management.

Safety Critical Items: These are items requiring a high level of integrity because of

their criticality for the safe operation of the railways. Therefore, all aspects of the

management of these items, from design through to operation and maintenance, are

subject to stringent controls. In addition to requirements of the Safety Modules,

comprehensive standards are prescribed for the design, operation, and maintenance

of these items.

Safety Committees: A Corporate Safety Committee will be established to oversee

safety governance at corporate level. Reporting to the Corporate Safety Committee,

divisional safety committees are established to support line management in

discharging their safety management responsibilities. The Safety Committee for the

railway is supported by a number of sub-committees, each with their respective

functions, e.g. reviewing, developing and proposing safety.

Staff Consultation: Safety is a standing agenda item in line management meetings

at all levels of the organisation and safety topics are discussed regularly at divisional

level communications. Regular safety briefings and pre-work safety talks are held for

different work teams. Furthermore, Staff Consultative Committees will be formed

and they are mechanisms for consultation with staff to provide a means for

management and staff to freely exchange views on safety and health matters. In

addition, large-scale educational and promotional programs may be held periodically

to enhance staff’s safety awareness and knowledge. For example, the programs

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include an annual corporate event enhancing staff’s and contractors’ safety

awareness through safety seminars and exhibitions. A Safety and Quality Quiz and a

First Aid Competition are organised to enhance staff’s safety, health and first aid

knowledge and skills, which is useful to deliver an even higher quality service at

work. In order to update safety awareness of passengers on a regular basis, some

annual events are held, e.g. the safety awareness of passengers travelling on the

railway. Moreover, a few programs are targeted for special passengers groups which

address to their concerns on safety particularly. For example, Youngster Kit and

Elderly Kit have been produced for school children and elderly, on-line interactive

safety games and regular visits to schools and elderly / community centres enhance

their understanding on the proper and safe ways of travelling on the railway.

2.5.4 External Bodies Assisting in Rail Safety

Serious rail accidents, such as derailments and collisions which resulted in fatal

consequences, occur rarely but when they occur they attract the interest of the public

and safety professionals all over world. In order to avoid such accidents or to

minimise the consequences in the event of accidents occurring, a group of external

bodies (who are safety authorities and independent from railways) assist in various

ways to enhance the safety environment in railways. Following are some of the

external bodies and their responsibilities regarding the assistance of safety

improvement.

Accident and Incident Investigating Bodies: Criteria governing the independence

of the investigating body are strictly defined so that this body has no link with the

various areas of the sector. This body decides whether or not an investigation of such

an accident or incident should be undertaken, and determines the extent of

investigations depending on consequences and the necessary procedures to be

followed. The investigations need to be carried out with as much openness as

possible, so that all parties can be heard and can share the results. The relevant

infrastructure manager and railway undertakings, the safety authority, victims and

their relatives, owners of damaged property, manufacturers, emergency services

involved and representatives of staff and users should be regularly informed of the

investigation and its progress. Each investigation of an accident or incident will be

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the subject of reports in a form appropriate to the type and seriousness of the accident

or incident and the importance of the investigation findings. Each country should

ensure that investigations of accidents and incidents are conducted by a permanent

body, which comprises at least one investigator able to perform the function of

investigator-in-charge in the event of an accident or incident.

Rail Safety Certification: It is a requirement that a railway undertaking (governing

bodies and other stakeholders) holds a safety certificate before it is granted access to

the railway infrastructure. This safety certificate may cover the whole railway

network or only a defined part thereof. The fact that national safety certificates differ

is an obstacle to the development of the international railway system. The ultimate

objective is to introduce a single community certificate. In other words, if a railway

undertaking obtains a safety certificate in a country, that certificate should be the

subject of mutual recognition anywhere in the world. The safety certificate should

give evidence that the railway undertaking has established its SMS and is able to

comply with the relevant safety standards and rules. For international transport

services it should be enough to approve the SMS in a country. Adherence to national

laws on the other hand should be subject to additional certification in each country.

The safety certificate must be renewed upon application by the railway undertaking

at regular intervals. It must be wholly or partly updated whenever the type or extent

of the railway operation is substantially altered. A railway undertaking applying for

authorisation to place rolling stock in service will submit a technical file concerning

the rolling stock or type of rolling stock to the relevant safety authority, indicating its

intended use on the network. In addition to the safety requirements laid down in the

certificate, licensed railway undertakings must comply with national requirements,

compatible with international law and applied in a non-discriminatory manner,

relating to health, safety and social conditions, and the rights of workers and

consumers. An essential aspect of safety is the training and certification of staff,

particularly of train drivers. The training covers operating rules, the signalling

system, the knowledge of routes and emergency procedures.

National Safety Authority: Each state within a country will establish a safety

authority (for example, WorkCover Authority (WCA); Independent Transport Safety

and Reliability Regulator (ITSRR) in New South Wales, Australia), which is

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independent from railway undertakings, infrastructure managers, applicants for

certificates and procurement entities. It will respond promptly to requests for

applications, communicate its requests for information without delay and adopt its

decisions after all requested information has been provided. The safety authority will

carry out all inspections and investigations that are needed for the accomplishment of

its tasks and be granted access to all relevant documents and to premises,

installations and equipment of infrastructure managers and railway undertakings.

Each year the safety authority should publish a report concerning its activities in the

preceding year.

2.5.5 Need for Measuring Rail Safety

As societies become more affluent their levels of mobility also increase. While

greater mobility is to be encouraged, there are risks associated with travel. Safety

measures need to be taken to decrease the propensity to incur accidents. This is a

common practice in nations that have been motorised for many decades and

transportation-related accidents and fatalities have been studied and modelled for

decades (Soot, Metaxatos & Sen 2004). The need for measuring safety arises to

assess the level of Safety on a railway network, to help management decide resources

allocation by providing “what if” data, and to identify weak links in the SMS. As

quoted by Lord Kelvin “When you can measure what you are speaking about and

express it in numbers you know something about it; but when you cannot measure it,

when you cannot express it in numbers, your knowledge is of a unsatisfactory kind.”

Statistical analysis is one of the key methods to monitor safety performance levels

and to benchmark trends within the industry. Shall we consider accident statistics as

safety performance indicator? They provide a cost effective measure of performance

in terms of the cost associated with data collection, but they suffer from several

limitation, which should be taken into account while assessing an organisation’s

safety performance. Statistics conceal a lot more than what they reveal, which are the

most charitable remarks about statistics. It is further argued that accident statistics

measure only failures. These are ‘trailing indicators’ and not ‘leading indicators’.

Thus the utility of accident statistics as a measure of safety in a railway network is

extremely limited. So how do we measure safety performance better? It is stated that

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for the purpose of measuring Safety, ‘leading indicators’ will provide a better

system. The Rail SMS of measuring Safety should meet the following two criteria:

• Validity – the extent to which the measurement reflects the true ground

conditions; and

• Reliability - the extent to which the system of measurement gives the same

results on successive occasions of use.

Safety in the Rail SMS, a railway network or otherwise, has to be an integral part of

processes, methods, equipment, materials, people, etc. Logically measuring safety

should be concerned with the quantity and quality of the activity in these areas as

well as measuring events such as accidents, averted accidents, other incidents,

equipment failure, etc. Safety is not a directly measurable entity in the same manner

as, for example, profit or loss of an organisation. It is more constructed, and reflects a

sphere of activity concerned with the reduction of risk and the reduction of the

consequences of the unwanted events.

2.5.6 Risk Assessment in Rail SMS

The Rail sector will provide both strategic and operational management services that

underpin the risk management process.

• Development of management systems and assurance processes in close

conjunction with client requirements

• Due diligence studies to identify risk exposures and develop plans for

ongoing management control and implementation of process improvements

• Validation of organizational change and development of SMS, procedures

and risk management arrangements

• Management reviews and use of Pharos system to manage workplace

hazards.

Assessment of risk is an important process in SMS. The Rail sector's core objective

is assessing and prioritising these risks to passengers, the public and railway

employees and to put in place recommendations and actions to help eliminate their

underlying causes and effects. It should bring together engineering and management

skills to assess risk and develop cost-beneficial risk reduction strategies.

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• Hazard identification using techniques such as task analysis, audit, etc.

• Human factors assessments

• Reliability, availability, maintainability and safety studies

• Quantitative evaluation of risk using tools such as fault and event trees

• Qualitative risk assessment

• Risk ranking.

Change Management: The sector should provide interpretation of client objectives,

development of close partnerships with clients and risk based change solutions. It

may also provide support from senior managers with industry experience to assist

with implementation of the change.

Safety Case Support: The sector will provide an unrivalled service for the co-

ordination, planning, preparation and ongoing support for all aspects of the Railway

Safety Case.

• Safety Case program management

• Risk assessments of changed operations, methods and management structures

for inclusion in the Safety Case

• Audit against the provisions of the Safety Case

• Safety Case peer review, understanding of issues, and recommendations for

improvement implementation

• Training of staff at all levels in the concepts and applications of Safety Case

• Development of emergency plans

Specialised Engineering Analysis & Risk-based Inspection: The railway’s multi-

disciplined engineers should have extensive experience in the practical application of

advanced analysis techniques to solve real engineering problems and provide real

engineering answers.

Safety Information Database: In order to improve rail SMS, it is necessary to

maintain an effective safety information database and to have access to continuously

updated information on each and every area of rail operations. For example,

information in the area of grade crossing operations such as detailed grade crossing

inventories, details of accident circumstances, accidental causes, casualties, details of

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the growth in the highway and rail traffic passing through should be maintained and

updated in the safety information database. In general, the main purpose of

maintaining the safety information database is to provide search capabilities for

information and compile various statistics related to events on railway accidents /

incidents. The information stored in the database may be used to:

• Provide feedback and exchange information promptly

• Draw up statistics to conduct analysis

• Conduct risk assessments and

• Enhance proactive safety management.

2.6 Major Safety Issues at Railway-Highw ay Interfaces

Railroad transportation became one of the major factors in accelerating the expansion

of a country’s economy by providing a reliable, economical and rapid method of

transportation. Today, railroad transportation facilitates the establishment and growth

of towns in a country by providing a relatively rapid means of transportation of

passengers. Additionally, they are major movers of fuel, coal, ores, minerals, grains

and farm products, chemicals and allied products, food and kindred products, lumber

and other forest products, motor vehicles, heavy equipment and bulk materials. New

towns are generally developed along the railway line as they heavily depend on

transport services. In the east, railroads were built to serve the existing towns and

cities. Many communities wanted a railroad and certain concessions were made to

obtain one. Railroads were allowed to build their tracks across existing roads and

highways at-grade, primarily to avoid the high capital costs of grade separations. As

people followed the railroads to the west there was a need for new roads and

highways, most of which crossed the railroads at-grade.

In earlier days, safety at railway-highway grade crossings was not considered a

problem. Trains were very few and relatively slow, as were highway travellers who

were usually on foot, horseback, horse-drawn vehicles, or cycles. By the end of the

century, as crossing accidents were gradually increasing, communities became more

concerned about safety and operations at grade crossings. In some countries, a very

large number of railroad accidents and heavy accidental consequences are now

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associated with railway-highway crossings. For example, grade crossing accidents on

Indian Railways accounting for 22% of the total rail accidents were responsible for

49% of total fatalities during the last decade (Verma 2007, p.1). Level crossings are

responsible for more than 23% of the train accident risk factors present on the British

Rail Network (Rail Safety & Standards Board 2004). A set of statistics on accidents

at level crossings and consequences from some selected countries are provided

below. These statistics suggest that efforts are needed to develop effective

countermeasures to reduce crossing accidents. Many countries adopted laws,

ordinances and regulations to provide safety improvements on operations at the

crossings. In fact, the railway-highway interface is unique in that it constitutes the

intersection of two individual transportation modes which differ both in the physical

characteristics of their travelled ways and their operations. Accidents at railway-

highway crossings cause huge damages and losses including passengers, members of

the public, rail workers and properties such as rolling stocks, road vehicles, rail

infrastructures, etc. Safety levels at railway-highway interfaces continue to be of

major concern despite improved design and application practices.

2.6.1 Statistical Overview of Gl obal Level Crossing Collisions and

Consequences

This section presents an overview of global highway - railway grade crossing

accidents and their consequences in the past few years, from both qualitative and

quantitative perspectives. It assists in comparing the risks at level crossings in

various countries around the world. For the purpose of overview, level crossing

collisions and consequences over fifteen selected countries are considered. Statistical

details of “highway-railway” grade crossings accidents and consequences resulted

from those accidents are reported as given below.

United States: There are 241,817 railway-highway grade crossings (including

146,103 public, 93,689 private and 2,025 pedestrian) in the USA. Each year, about

368 people lose their lives and 1,057 people are injured as a direct result of grade-

crossing collisions occurring at the annual rate of 3,081 approximately (USDOT

FRA accidents database, 2006).

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Canada: Within 10,381 unique crossings in Canada, a total of 1,724 collisions were

reported over a nine-year period (1993-2001). These collisions resulted in

242 fatalities and 347 serious injuries (Department of Civil Engineering, University

of Waterloo, 2003).

Japan: In Japan, there are currently about 37,326 level crossings of all types. Over a

nine-year period (1990-1998), 5,352 level crossing accidents were reported which

resulted in 1,387 fatalities and 2,171 injuries (Transportation Ministry, Japan, 2001).

New Zealand: There are 1,398 level crossings over the New Zealand railway

network. Between 2001 and 2003 there was an average of 30 collisions. There were

six fatal, five serious injury and four minor injury crashes per year at these level

crossings (Patterson 2004).

Australia: There are approximately 9,400 public railway level crossings in Australia

(Australian Transport Council, 2003). Over a seven-year period (2001-2007), a total

of 551 level crossing accidents were reported which resulted in 259 fatalities

(Australian Transport Safety Bureau, 2008). In the state of New South Wales, there

were 267 level crossing crashes reported over the period of 12 years (1990-2001)

which resulted in 50 fatalities.

Selected Ten European Countries: Figures for the number of level crossings,

annual average number of collisions and fatalities for a selection of ten European

countries are given in Table 2.5 (Rail Safety & Standards Board, 2004).

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Table 2.5: Level Crossing Accident Statistics in Selected European Countries

Country Number of Level

Crossings

Annual Average

Collisions

Annual Average

Fatalities

Belgium 2,409 62.86 14.29

Finland 5,283 48.57 9.86

France 19,831 178.29 49.71

Great Britain 8,323 30.29 8.57

Germany 26,980 451.80 91.20

Ireland 1,976 4.14 0.57

Luxembourg 149 2.00 0.57

Netherlands 3,006 74.43 27.43

Portugal 2,972 117.20 24.00

Sweden 10,000 30.00 8.57

It can be noted from above overview that many countries show different statistics on

the rates of annual accidents and consequences at railway-highway grade crossings.

However, the USA has exceptionally highest figures compared to other countries.

2.6.2 Global Comparison of Level Crossing Accidents

Railway level crossing accidents are one of the major contributing factors of railway

related fatality problems in many countries (Zaharah 2007, p.1). Even though railway

level crossing accidents can be considered as a rare event, the impact is often severe.

The aim of this section is to compare the number of collisions and fatalities that

occurred at level crossings in fifteen different countries around the world. However,

it should be remembered that there may be major differences between the various rail

networks worldwide and how many incidents may be recorded.

2.6.2.1 Level Crossing Collisions

Figures 2.9 and 2.10 show the data ordered in decreasing safety risk rates per

selected countries for collision and fatality respectively. The safety risk rate for

collision (Annual Collision Rate) for a country is calculated as the number of average

annual collisions per the number of level crossings in the country. In the similar way,

the safety risk rate for fatality (Annual Fatality Rate) for a country is computed as the

number of average annual fatalities per the number of level crossings in the country.

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Annual Collision Rates for Selected Countries

0

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Figure 2.9: International Comparison of Annual Collision Rate for Level Crossings

2.6.2.2 Level Crossing Fatalities

In comparing the number of collisions and fatalities, USA, Japan and Germany

appear to be the top three in ranking order. The reason for the high number of

collisions and fatalities in these countries is due to the high number of level

crossings. For example, the USA has the highest number of annual collisions (3,081)

and fatalities (368) as it has the highest number (241,817) of railway-highway grade

crossings.

Annual Fatality Rates for Selected Countries

0

50

100

150

200

250

300

350

400

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Figure 2.10: International Comparison of Annual Fatality Rate for Level Crossings

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However, in comparing both collision and fatality rates among the 15 countries,

Netherlands, Portugal, Belgium and New Zealand appear to be the top four countries

in the risk ranking order. In the meantime, Great Britain, Sweden and Ireland seem to

be the bottom three countries in the risk ranking order. Australia sits in twelfth place

in the collision risk ranking. However, in the fatality risk ranking, Australia takes

sixth place. This shows that even though the occurrence of railway level crossing

accidents in Australia is at a low frequency rate, its consequences (especially

fatalities) seem to be more severe. The loss due to these accidents is very significant

and has a huge negative impact on the Australian economy. Therefore railway level

crossing accidents are one of the most serious safety issues faced by the rail system

in Australia and many similar countries around the world.

2.7 Background of Research Problem

The previous section explained the major safety issues at level crossings in various

countries in detail. The railway-highway level crossing is a special type of

intersection. The fact is that trains run on a fixed guide way and cannot avoid

collision. In most cases, trains are not expected to stop and yield to motorists and

some trains would require several kilometers to stop. Some train speeds can be

considerably higher than normal road speeds. In comparison with the studies

conducted regarding highway traffic safety, there have been few studies involving

motor vehicles and train accidents. Even though an accident involving motor

vehicles and trains is not of great concern at present, it is important to remember that

when there is an accident involving a motor vehicle and a train, the rate of severity

and the cost involved can make a greater impact to the country since it results in

property damages and loss of lives. As highlighted by the Australian Transport

Council (2003) in the National Railway Level Crossing Safety Strategy Report,

accidents at railway level crossings make a greater impact on everyone involved,

especially when it results in a fatality. It will result in incalculable pain and suffering

for families and others associated with victims as well as any operator staff involved

in the crash. Direct financial costs in term of medical and repair costs, loss of

personal income and loss of business and consequential financial loss are also the

result of these accidents.

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2.7.1 Significance of Safety Im provement at Level Crossings

Global rail industry sectors continue to facilitate national safety improvement plans,

strategies and intervention programs to further improve safety for the workforce,

passengers and the wider public. In order to identify the worst safety performances or

higher risk areas, comprehensive and improved methodologies / approaches are

consistently needed to measure safety performance systems and to assess risk

potentials in various parts of railways. The railway-highway grade crossing is unique

in that it constitutes the intersection of two transportation modes which differ both in

the physical characteristics and in their operations (Federal Highway Administration

1986, p.1). Grade crossing accidents not only dominate in terms of frequency, but

can be more severe in their consequences than other types of railway accidents in

several developing and developed countries. This is because these accidents can

involve injuries and fatalities to railway passengers as well as to highway vehicle

occupants and other grade crossing users.

Level crossings now have the potential to become the largest single cause of

potentially catastrophic train accidents on the railway. Abuse of level crossings by

road users and pedestrians is also a significant cause of individual accidents to the

public and creates additional risk for rail users and staff. Additionally, increasing

road construction and road vehicle population create greater opportunity for grade

crossing accidents to happen. Both railway and highway operators are committed to

grade crossings safety. Since oncoming trains cannot stop for highway vehicles

whose drivers violate highway safety laws when approaching railroad tracks, each

grade crossing presents possible danger to motorists, vehicle occupants and train

drivers. It is therefore important to identify and implement improved ways of

reducing these risks to make them as low as reasonably practicable.

2.7.2 Previous Research on Risk Assessment at Grade Crossings

In the past few years, a considerable number of research studies were conducted to

develop appropriate statistical models to assess the risk at grade crossings and to

identify black-spots (worst performing crossings). For example, the University of

Waterloo Canada developed an appropriate risk model for targeting black-spot

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crossings in Canada (Saccomanno et al. 2003). The appropriate allocation of safety

improvements to level crossings to reduce the accidents and consequences is a

difficult task. Accident experience alone fails to provide a good appreciation of

future expected accidents at level crossings (Saccomanno, Fu & Miranda 2004). This

is because accidents at level crossings are rare, random events which vary over time

and space. The expectation of accidents and its severity can only be obtained from

accurate and reliable collision and consequence prediction models. The development

of such models allows the appropriate prioritisation of safety improvements.

In order to enhance grade crossing safety, there is a need to have improved safety

risk assessment methodologies, associating with rail SMS, which can help in taking

necessary cost effective measures to reduce accidents and their severity. In

implementing a risk assessment process, statistical modelling of traffic accidents has

been of interest to researchers for decades (Mitra & Washington 2006, p.1).

Moreover, the statistical approaches have generally included Poisson and Negative

Regression Models (Caliendo, Guida & Parisi 2006, p.657).

2.7.3 The Need for Improving Ra ilway Grade Crossings Safety

Details about the significance of improved safety at level crossings due to existing

potential risk hazards were presented earlier. Thus improving safety at level

crossings is one of the key contributing factors to enhance railway safety worldwide.

In particular, it was noted earlier that Australia takes twelfth place in the collision

risk ranking and sixth place in the fatality risk ranking by comparison with other

countries. This indicates that whilst the occurrence of rail grade crossing accidents in

Australia is at a low frequency rate, the accidental consequences are severely high.

Therefore, the accidental loss is a significant issue and has a huge negative impact on

the Australian economy.

In the approach from the University of Waterloo Canada, accidents frequency and

accidental consequences were considered of equal importance in the model

development and thus assigned the same value (Saccomanno et al. 2003). In order to

allow for more generalised situation of accidents frequency and the accidental

consequences, this study proposes a new improved quantitative risk assessment

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approach where two key indicators (accidents frequency and accidental

consequences) are combined to make a single risk measure (Safety Risk Index). This

approach of combining two indicators is investigated further through model

development and verification using a set of test data for predicting accidents and

consequences with accurate black-spot identification.

The main goal of the quantitative risk assessment on grade crossings is to estimate

collective risk of accidents and consequences at rail crossings. The risk assessment

models are developed using data and information associated with accidental events

that have occurred over past few years in the USA. The statistical analyses of data

and information, reports and information are combined with occupational health and

safety performance, safety intelligence, and emerging trends in rail SMS for decision

making on various aspects of rail safety. The proposed methodology and the risk

assessment models developed in this study will provide support to rail industry

groups in national safety improvement plans which address major areas of safety

concerns and issues, to facilitate the effective representation of the rail industry in the

development of national legislation and standards that impact on the railway-

highway grade crossings. Thus, the main purpose of this research study is to:

• Identify and analyse the generic residual safety risks associated with Rail

sector’s operations and their rail SMS in place;

• Review systematically the safety risk potentials at railway-highway grade

crossings and identify current accidents trends by analysing accident events

and precursors;

• Quantitatively assess and prioritise the residual safety risk potentials at

railway-highway grade crossings;

• Identify the worst performing locations (black-spots) and analyse the

important factors which influence the safety risks at those crossings;

• Report the findings to the rail industry in order to undertake safety

improvement plans, strategies and intervention programs to reduce the safety

risks at those identified black-spots.

Recognising this existing potential risk hazards at level crossings, this research study

is fully committed to railway-highway grade crossing safety. This study presents an

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improved methodological approach for assessing railway level crossing safety risks.

Due to the complex nature of level crossing safety systems a quantitative risk

assessment approach is applied in assisting the development of a meaningful

comprehensive safety risk model. The basic concepts for safety measures (frequency

of collisions and consequences) are considered in the model development.

2.8 Summary

Overall, this study identifies and analyses the general safety risk on railway-highway

crossings, characteristics of the crossing environment and their users, and the

physical and operational improvements that can be made at railway-highway

crossings in order to enhance safety and operations of both highway and railway

traffic at crossings. In broader sense, this research seeks to fill some of the

knowledge gaps on complex relationships between collisions involving road vehicles

and trains and consequences of those accidents, and to assess the safety risks at

interface locations through the application of risk assessment models. The risk

assessment models are developed using crash/accident data, characteristics of

railway-highway crossings and influencing factors identified, based on a selected test

case. A quantitative risk index method is developed for effective countermeasures to

reduce crossing accidents. The proposed approach with a quantitative model of risk

assessment and risk index is integral part of continuous improvement method for

accurately estimating safety level at each railway-highway crossing across a large

network. The proposed model is used to analyse each potential area of accidents in

terms of frequencies and consequences and subsequently safety risk index rating.

This safety risk index rating process identifies the strengths as well as the

weaknesses of the crossing’s safety systems and operations activities.

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Chapter 3

Research Methodology

3.0 Introduction

The previous chapter overviewed the current safety issues in the Rail sectors and the

safety management systems in place. It also identified the major safety issues and the

significance on improving the safety at level crossings. In order to address those

safety issues identified through a risk assessment model and its application, the

research methodology adopts a two-step process. The initial step in the process of

improving the safety is to develop a theoretical framework on safety risk evaluation

at rail grade crossings. This is followed by developing a risk assessment model,

based on the risk factors influencing accidents at grade crossings.

Thus, this chapter introduces all procedures and steps involved in development of

research methodology for assessing safety risks at the grade crossings. This

includes: Overview of fundamental concepts of safety risk evaluation; developing

theoretical framework on safety risk evaluation at rail grade crossings; Current

statistical models used for predicting highway accidents; and Evaluation of risk at

grade crossings with application of safety risk index. Further, the chapter explores

the risk factors influencing accidents at railway-highway interfaces. It also

overviews the existing models developed for prediction of collisions and

consequences. Finally, it develops an improved risk assessment method to assess and

to prioritise risks at grade crossings.

3.1 Fundamental Concepts on Safety Risks Evaluation

In general, every organisation is committed to providing a safe, efficient and reliable

network and working environment for their employees, customers and the general

public. However, organisations are always exposed to an endless number of new or

changing risks that may affect its operation or the fulfilment of its objectives

regarding safety. The only way to understand and assess the impact of the risk

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involved in an organisation and hence to decide on the appropriate safety measures

and controls to manage them are obtained by conducting the processes of

identification, analysis and evaluation of these risks. It is noted that Risk Assessment

is a process that in many cases is not or at least not adequately carried out, even if

Risk Management is introduced.

In recent years there has been increasing emphasis on SMS and associated practices

and issues in various industries and applications. In this context, various kinds of

regulation have emerged specifying how organisations must manage health and

safety (Hopkins & Wilkinson 2005, p.4). These systems are developed through

application of continual improvement cycle of monitoring and review on safety

performance. In general, when SMS are prescribed for addressing safety issues and

are required by regulatory requirements, they are generally risk-based. As a result,

organisations need to go through the process of risk identification, risk assessment

and risk control.

3.1.1 Identification of General Risks

The first phase is the identification of threats, vulnerabilities and the associated risks.

A systematic and comprehensive process of risk assessment needs to be carried out

in order to ensure that no risk is unwittingly excluded. During this process, all risks

should be initially identified and recorded in a comprehensive list. Some of the risks,

recorded in the list, may already be known and most likely controlled by the

organisation. The list should also contains the information such as sources of risks

and events that might have an impact (such as preventing, degrading, delaying or

enhancement) on achieving system and/or organisation objectives. A risk can

generally be characterised by or related to the following (Risk Assessment n.d.).

• Origin or source of the risk (e.g. threat agents such as hostile employees or

employees not properly trained, competitors, governments, etc.);

• Certain activities, events or incidents (e.g. unauthorised dissemination of

confidential data, competitor deploys a new marketing policy, new or revised

data protection regulations, an extensive power failure);

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• Consequences, results or impact of the risk (e.g. service unavailability, loss or

increase of market/profits, increase in regulation increase or decrease in

competitiveness, penalties, etc.);

• Specific reason for its occurrence (e.g. system design error, human

intervention, prediction or failure to predict competitor activity);

• Protective mechanisms and controls together with their possible lack of

effectiveness (e.g. access control and detection systems, policies, security

training, market research and surveillance of market); and

• Time and place of occurrence (e.g. during extreme environmental conditions

there is a flood in the library).

Thorough knowledge and detailed information of the organisation and its internal

and external environment play important roles in identifying risks. Past historical

information about the organisations can be very useful as they can lead to accurate

predictions about current and evolving issues that have not yet been faced by the

organisation. There are many ways an event can occur that makes it important to

study all possible and significant causes and scenarios. Checklists, judgments based

on experience and records, flow charts, brainstorming, systems analysis, scenario

analysis and systems engineering techniques are included in methods and tools used

to identify risks and their occurrence. The following techniques need to be

considered in selecting a methodology of risk identification (Risk Assessment n.d.).

• Team-based brainstorming (where workshops can prove effective in building

commitment and making use of different experiences); and

• Structural techniques (such as flow charting, system design review, systems

analysis, hazard and operability studies, and operational modelling).

3.1.2 Evaluation of Risks

In the phase of risk evaluation, decisions have to be made concerning which risks

need treatment and which do not, as well as the treatment priorities. The level of risk

determined need to be compared during the analysis phase with risk criteria

established in the Risk Management context. The risk evaluation of some cases may

lead to a decision to undertake further analysis. The criteria used in analysis phase

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have to take into account the organisation’s objectives, the stakeholder views and the

scope and objective of the Risk Management process itself. In general, the decisions

made are usually based on the level of risk. However, they may also be related to

thresholds specified in terms of the following (Risk Assessment n.d.).

• Likelihood of events;

• Consequences of the events (e.g. impacts);

• Cumulative impact of a series of events that could occur simultaneously.

3.1.3 Analysis of Risk

In the risk analysis phase, the level of risk and its nature need to be assessed and

understood. This information initially assists the decision makers making decisions

on whether risks need to be treated or not and what the most appropriate and cost-

effective risk treatment methodology or intervention program is. The process of risk

analysis includes (Risk Assessment n.d.):

• Examination of the risk sources;

• Analysis of their consequences (positive or negative);

• Evaluating the likelihood that those consequences may occur and the factors

that affect them;

• Assessment of any existing controls or processes that tend to minimise risks

(these controls may derive from a wider set of standards, controls or good

practices selected according to an applicability statement and may also come

from previous risk treatment activities).

Thus, the level of risk can be estimated using statistical methods and numerical

evaluations combining impact and likelihood. Appropriate formulas and methods for

combining them need to be consistent with the criteria defined when establishing the

Risk Management context. The reason for this is that since an event can have

multiple consequences and affect different objectives, consequences and likelihood

are to be combined to calculate the level of risk. If there is no reliable or statistically

reliable and relevant past data available, other estimates can be made as long as they

are appropriately communicated and approved by the decision makers. All necessary

data and information used to estimate impact and likelihood usually come from (Risk

Assessment n.d.):

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• Data and records or past experience (e.g. risk register, incident reporting);

• Expert advice and specialist;

• Engineering, economic or other models.

• Market research and analysis;

• Experiments and prototypes; and

• Reliable practices, international standards or guidelines.

In general, risk analysis includes techniques such as (Risk Assessment n.d.):

• Interviews with experts in the area of interest and questionnaires;

• Use of existing models and simulations;

• Development and use of appropriate quantitative risk assessment models.

In this research study, development and use of appropriate quantitative risk

assessment models (the last one in the list above) is chosen as the basis for assessing

and prioritising the risks at grade crossings.

3.1.4 Types of Risk Analysis Methods

Selecting appropriate method for risk analysis varies, depending on the nature of

risk, the purpose of the analysis, and the required protection level of the relevant

information, data and resources. It is essential to match the risk assessment method to

the objective of the risk analysis and expected deliverables. It is very important to

note that the quality of risk assessment deliverables is greatly influenced by selecting

the appropriate method to review the system or issue identified. As seen in Figure 3.1

there are three common types of risk analysis methods (Joy & Griffith 2007, p.48):

• Qualitative;

• Quantitative; and

• Semi-Quantitative.

In any case, the type of analysis performed will be consistent with the criteria

developed as part of the definition of the Risk Management context. A brief

description of the above-mentioned types of analysis is given below.

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1.Qualitative Types of

Risk Analysis

2.Quantitative 3.Semi- Quantitative

Figure 3.1: Three Common Types in Risk Analysis Methods

3.1.4.1 Qualitative Risk Analysis

Qualitative risk analysis describes the magnitude of potential consequences and the

likelihood that those consequences may occur, using appropriate scales. The scales to

describe the magnitude of potential risks can be adapted or adjusted to suit the

circumstances. Therefore different descriptions may be used for different risks. This

method is used to set priorities for various purposes including further analysis. For

the purpose of illustration, probability and consequences of an event are grouped into

a set of identifiers and are shown in Tables 3.1 and 3.2 respectively. Based on those

groups defined, qualitative analysis can generally be used:

• As an initial assessment to identify risks which will be the subject of further

detailed analysis;

• Where non-tangible aspects of risk are to be considered.

• Where there is a lack of adequate information and numerical data or

resources necessary for a statistically acceptable quantitative approach.

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Table 3.1: Group Selection for Estimating Probability of an Event

Identifier Descriptor

Very likely Very common event or very likely to occur (p > 0.1)*

Likely Probably will occur or “it has happened” (0.1 > p > 0.01)

Possible May occur or “heard of it happening” (0.01 > p > 0.001)

Unlikely Not likely to occur or “never heard of it” (0.001 > p > 0.000001)

Highly unlikely Practically impossible (0.000001 > p)

* Unwanted event expected to happen 1 in 10 times the circumstances occur.

Table 3.2: Group Selection for Measuring Consequences of an Event

Identifier Descripto r

Fatality Catastrophic or fatal event

Major injury Critical serious injury yields permanent disability

Minor injury Moderate or average lost time injury occurs

First aid only First aid given to minor injury

Negligible No injury at all

It is noted that there are many variations on design of qualitative analysis approaches

(Joy & Griffith 2005). However, the description or numerical ranges are required to

be carefully defined to meet objectives as well as to provide discrete and suitable

choices. Qualitative analysis is useful when reliable data for more quantitative

approaches is not available. Some techniques outlined below are suitable for

categorising risks on the basis of individual or team opinion. Further, differences

between categories (high, medium, low, etc.) are difficult to define and quantify as

they simply describe using qualitative terms. Therefore it remains for the individual

who uses this method to decide those differences. As such, it generally can be

considered a rough method of risk analysis that simply divides the identified risks

into four categories:

• Extreme;

• High;

• Medium or Moderate; and

• Low.

Once the probability and consequences of an event are chosen, a comparative risk

rank matrix can be developed as shown in Table 3.3 (Joy & Griffith 2005). The

details of each element of the matrix are given in below the table.

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Table 3.3: A Typical Qualitative Risks Ranking Matrix

Likelihood (Probability)

Consequences (Severity)

Negligible First aid only

Minor injury

Major injury Fatality

Very likely M H H E E

Likely M M H H E

Possible L M M H H

Unlikely L L M M H

Highly unlikely L L L M M

Identifier Risk Level Risk Control Measures

E Extreme risk

• Activity must not start or if started, must be stopped; • Immediate action required; • Notify supervisor or appropriate Health and Safety Authority as required; • Highest level corporate management needs to be involved; • Identify hazards and implement controls to reduce risk to low before starting or recommencing activity.

H High risk • Activity must not start or if started, must be stopped; • Immediate action required; • Notify supervisor as required; • Senior site management needs to be involved; • Identify hazards and implement controls to reduce risk to low before starting or recommencing activity.

M Moderate risk

• Immediate action to minimise injury e.g. signs; • Supervisor remedial action required within 5 working days; • Complete risk assessment needed; • Identify hazards and implement controls to reduce risks; • Management responsibility must be defined. L Low risk • Remedial action within 1 month, supervisor attention required; • Identify hazards and implement controls as required; • Manage by routine processes.

3.1.4.2 Quantitative Risk Analysis

Numerical values are assigned to both impact and likelihood in quantitative analysis

(Joy & Griffith 2005). In general, these values are derived from a variety of sources.

Further, the quality of the entire analysis depends on the accuracy of the assigned

values and the validity of the statistical models used. Impact can be determined by

evaluating and processing the various results of an event or by extrapolation from

experimental studies or past data. Consequences can be expressed based on various

terms of following impact criteria.

• Monetary;

• Technical;

• Operational; and

• Human.

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Quantitative risk analysis, based on (reference to the above) involves the calculation

of probability of unwanted events and subsequently the probability of consequences

from those events, using numerical data where the numbers are real numbers (i.e. 1,

2, 3, 4, etc. where 4 is twice 2 and half of 8) but rather are not in ranking order (i.e.

1st, 2nd, 3rd etc.). As such, accurate quantification of risk offers the opportunity to

be more objective and analytical than the qualitative approach. Most commonly,

quantification of risk involves generating a number that represents the probability of

a selected consequence of an event, such as a fatality. For example, Table 3.4 shows

a range of causes and corresponding probability of death in the UK over one year

period. British Nuclear Industry research reports the following probability of death,

based on historical data from various causes in the UK (Joy & Griffith 2007).

Another example, the risk of a total petroleum storage tank structural failure might

be .003 per year. If there are multiple events that must happen before a major loss

can occur, then assigning probabilities to multiple events allows for estimations /

calculations of risks that are normally not possible with qualitative or semi-

quantitative data.

Table 3.4: Probability of Deaths by Causes

Causes Probability of Death in the UK

Smoking 0.05 or 1 in 200

Mining Accidents 0.001 or 1 in 1000

Road Traffic Accidents 0.0001 or 1 in 10000

Industrial Accidents 0.00001 or 1 in 100000

Flying in Commercial Aircraft 0.00001 or 1 in 100000

Fire / Explosion at Home 0.000001 or 1 in 1 million

Lightning 0.0000001 or 1 in 10 million

Individual safety cases rely heavily on the selected risk assessment techniques and

some people see this as unsatisfactory (Hopkins & Wilkinson 2005, p.7). Complex

risk assessment methodologies, particular where quantification is involved, can be

difficult to understand for everyone. Not surprisingly therefore they may not be

trusted. Furthermore it is often suggested that quantitative risks assessments have

been massaged so as to reduce the risk to an acceptable level. Such misuse of risk

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assessment almost certainly occurs. However, this is a criticism of how risk

assessment is applied and not the concept itself. For example, in a complex plant

with complicated processes there is no alternative to the use of systematic hazard and

risk assessment methodologies. It is therefore expected that any kind of

methodologies, which are being developed to evaluate risks, need to be very simple

and easily understandable to people with different levels of knowledge on safety.

3.1.4.3 Semi-Quantitative Risk Analysis

The objective of semi-quantitative risk analysis is to provide an analysis using some

indicator values, which are assigned to the scales used in the qualitative assessment.

These values are usually indicative and are prerequisite of the quantitative approach.

Since the indicator value allocated to each scale is not an accurate representation of

the actual magnitude of impact or likelihood, the numbers need to be combined using

a formula that recognises the limitations or assumptions made in the description of

the scales used. It also needs to be mentioned that the use of semi-quantitative

analysis may lead to various inconsistencies due to the fact that the numbers chosen

may not properly reflect analogies between risks, particularly when either

consequences or likelihood are extreme. As noted in the above discussion on

qualitative and quantitative risk analyses, the specification of the risk level is not

unique. Impact and likelihood of an event can be expressed or combined differently,

depending on the type of risk, the scope and objective of risk management practices,

processes and systems.

3.2 Developing Theoretical Framework on Safety Risk

Evaluation at Rail Grade Crossings

There has been increased emphasis on rail safety management in recent years due to

the application of new legislations globally and the establishment of various SMS

standards. It has been determined from reported work that the risk assessment within

the broader area of risk management is a key process within a rail SMS. Further,

based on the facts and reasons outlined earlier in Chapter 2 on why level crossings

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now have the potential to become the largest single cause of potentially catastrophic

train accidents on the railway globally, this research aims to develop a theoretical

framework on safety risk evaluation at rail grade crossings. This is further endorsed

by the significance on safety improvement at level crossings identified earlier and the

need for developing an improved method to assess the risk at rail grade crossings.

This study therefore focuses on developing a framework to assess the residual risks

at railway-highway grade crossings and to prioritise these crossings in ranking order

using quantitative methods / models. In order to assess and to prioritise the risks at

grade crossings, three risk assessment models are developed and tested for their

validity using a comprehensive statistical analysis. The three risk assessment models

include (i) accident prediction, (ii) consequences estimation, and (iii) a combination

of the two models. The first two models are outlined with associated processes of

developing these models explained in Chapter 5. The final model, labelled “Safety

Risk Index (SRI)” is presented in Chapter 6.

3.2.1 Development of a Quantitati ve Risk Assessment Model for

Safety Evaluation at Rail Crossi ngs - Safety Risk Index (SRI)

As discussed earlier in the Chapter 2, there are two central principles in rail safety

evaluation: risk-based proactive and reactive approaches (Elms 2001, p.296). The

risk-based proactive safety approach is based on the implementation of modern

safety procedures and practices in rail operations. The risk-based reactive safety

approach is performed by analysing the past safety integration of data and

information for the different aspects of a rail safety system. For a reactive approach

in safety evaluation, rail accidents and their consequences are the direct measures of

rail safety. Since those accidents are random events, statistical models such as

Poisson or Negative Binomial can be utilised to generate mathematical models for

predicting accidents and consequences. The details of mathematical models,

including a brief introduction and background of models, objectives of the risk index,

the methodology for the development of the index, and some comparative results to

test on validity of the index are presented here.

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In general, it is common to discover facts about a real world phenomenon that

actually exists. The phenomenon is explained by collecting data from the real world

and then analysing this data to draw conclusions about the subject being studied. One

of a researcher’s tasks is to take available real world data and to use it in a

meaningful way. The nature of the tasks often involves building statistical models

under certain conditions and using them to make predictions about the real world

phenomenon of interest. The model may differ from reality in several ways. If we

want our inferences to be accurate, then our model needs to represent the data

collected as closely as possible. The degree to which the model represents the

observed data is known as the “goodness-of-fit” of the model (Wood 2002, p.419).

This section aims to provide a brief overview of some important statistical concepts

such as how statistical models can be developed, built and used.

3.2.1.1 Basic Concepts Used in Developing SRI

In order to provide rail safety evaluation from a quantitative perspective, the

fundamental elements associated with risk measurement need to be initially

identified. Based on research activities conducted by various researchers (such as

Saccomanno, F.; Xiaoming, L.; Buyco, C.; Miaou, S.P.; Lum, H.; Jovanis, P.P.; and

Chang, H.L. etc.) on quantitative safety risk modeling techniques, three basic

elements are identified. These three elements are:

• Exposure (E) - Measurement of exposure of rail users (employees, passengers

and the public) to potential railway hazards.

• Probability (P) - Measurement of the chance of rail users being involved in

potential railway accidents.

• Consequence (C) - Measurement of the severity level to rail users resulting

from potential railway accidents.

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1. Exposure (Exposure to hazards)

Safety Risk Index (SRI)

2. Probability (Likelihood of occurrence of an

accident)

3. Consequences (Severity of the accidental consequences)

Figure 3.2: Three Basic Elements of Measurement in the Development of SRI

It can be noted from Figure 3.2 that the safety risk index is influenced by three basic

elements of measurement. Therefore, Safety Risk Index (SRI) can be mathematically

expressed as:

(C)} eConsequenc (P),y Probabilit (E), {ExposureFunction = SRI (3.1)

Given safety risk assessment varies with the location of particular railway

infrastructure and the specific hazard, the index HazardSpecificithSRI defines the risk

associated with the specific hazard (thi ) and is derived by combining risk scores of

three basic elements of the hazard described above. The risk scores are the estimated

values, which are derived from predicted values of three basic elements using

mathematical models. The SRI for a specific hazard (thi ) can be defined as:

iiiHazardSpecificiCPESRI th **= (3.2)

where:

iE - the risk score due to exposure for thi hazard

iP - the risk score due to probability for thi hazard

iC - the risk score due to consequence for thi hazard

The overall risk index HazardsAllSRI defines the combination of risks associated with

all hazards within the location concerned. Hence, the SRI for combination of all

hazards at the location can be calculated using:

iii

n

i

HazardsAll CPESRI **1

∑==

(3.3)

Where, n - total number of hazards within the location concerned.

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3.2.1.2 Numerical Example on Application of SRI

As outline in the previous section, Safety Risk Index (SRI) is a function of

Exposure (E), Probability (P) and Consequence (C). In the case of safety risk

evaluation in rail infrastructure for a particular hazard (say collisions and their

consequences), three basic elements of measurement are illustrated using a simple

example as shown in Figure 3.3.

Figure 3.3: Graphical Representation of Three Elements of Safety Risk Evaluation at Two Types of Rail-Road Crossings

There are two different types of rail-road crossings noted from Figure 3.3:

• Crossing - 1 is a junction where animals, farmers and their vehicles cross a

railway track; and

• Crossing - 2 is a junction where highway vehicles cross the railway track.

Firstly, considering the first element of safety risk evaluation, it is considered that the

exposure (E) at Crossing - 2 is higher than that at Crossing - 1 (i.e. 2E > 1E ) as the

traffic volume or flow rate is much higher at Crossing - 2 than at Crossing - 1.

Secondly, probability (P) represents a measure to quantify chances of the occurrence

of an accident. In general, it is a random event and depends on several factors

including traffic-specific characteristics such as train speed and vehicle speed, and

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location-specific characteristics such as maximum protection types (crossing signs,

signals, gates, etc.). For the purpose of this discussion, it is assumed that the

probability of collision at Crossing - 2 is same as that at Crossing - 1 (i.e. 2P = 1P ).

Thirdly, in the event of a collision, the number of major injuries or fatalities per

accident would be minimal at Crossing - 1, since the number of vehicles and people

crossing here is relatively low compared with that at Crossing - 2. This means,

consequence (C) at Crossing - 2 is higher than that at Crossing - 1 (i.e. 2C > 1C ).

Mathematically, the Safety Risk Index (SRI) at Crossing - 1 for the hazard of

collisions and their consequences is given by the equation:

1111_sin ** CPESRI gCros = (3.4)

Similarly, the SRI at Crossing - 2 for the same hazard is written as:

2222_sin ** CPESRI gCros = (3.5)

Comparison of the index values at both crossings shows:

])/(*)/(*)/[(]/[ 1212121_sin2_sin CCPPEESRISRI gCrosgCros = (3.6)

Based on assumptions outlined above [i.e. 1)/( 12 >EE ; 1)/( 12 =PP and

1)/( 12 >CC ] it can obviously be noted that 1]/[ 1_sin2_sin >gCrosgCros SRISRI or

1_sin2_sin gCrosgCros SRISRI > . Based on this illustration and overall safety evaluation

using risk index values of all three basic elements (exposure, probability and

consequences), it may be concluded that Crossing - 2 has higher risk potential than

Crossing - 1 in relation to the hazard of collisions and their consequences.

3.2.1.3 Major Steps to Achieve Objectives of Study

It is evident from the literature review reported earlier that any program that attempts

to achieve safety improvement at grade crossings must be viewed as an integral part

of a comprehensive internationally identified multi-stage safety management

program, which generally consists of five major interconnected steps:

• Identifying crossings where the potential risk of accidents is unacceptably

high;

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• Reviewing the causes and consequences of accidents;

• Developing a model to assess and prioritise the risk potential at these

locations;

• Assisting in the development of cost-effective countermeasures aimed at

reducing risk at unsafe locations; and

• Assisting in the development of a comprehensive safety intervention program

at state and national levels that includes prioritisation of countermeasures at

high risk crossings.

Risk refers to both the likelihood of collisions and their consequent damages or

severity. Identifying risks potential, which is the focus of this study, reflects a long-

term stable likelihood that a certain risk exists at a given crossing over a period of

time and exposure. In many instances, the potential for collisions differs from the

historical collision experience. This is due to the fact that collisions are rare, random

events that fluctuate over time. Potential reflects a smoothing out of year-to-year

variations in the historical collision experience at each crossing location (De Leur &

Sayed 2002). One of the major characteristics of each crossing location that directly

relates to accidents is the identification of the location as a black-spot. Figure 3.4

shows the flow diagram of steps involved in identifying the black-spots. In this

research, risk assessment models are developed, using procedures outlined below:

• Review existing risk methodologies for predicting collision risk at “highway-

railway” grade crossings for different control factors and conditions;

• Review methodologies for identifying black-spots and prioritising safety

intervention;

• Develop a "risk-based" model for targeting black-spot crossings that are in

most need of safety intervention. Risk-based includes both the potential for

collisions at specific crossings (frequency), as well as the potential severity of

these collisions (e.g. fatalities, personal injuries, and property damages). The

model also includes objective measures of risk thresholds for prioritising

intervention;

• Apply the above model to grade crossings in order to obtain a prioritised list

of black-spots for safety intervention; and

• Investigate the major attributes of these black-spots in terms of geometry,

control devices and operating characteristics. Estimate the number of

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historical collisions and their consequences that would be flagged under the

proposed black-spot model.

Extracting Grade CrossingAccidents Data and Information

Extracting Grade CrossingInventory Data and Information

Data Source(U.S. Department of Transportation -

Federal Railroad Administration)

Developing Poisson, Negative Binomial and Empirical Bayesian

Models for Accidents Prediction and Consequences Estimation

Calculating Safety Risk Index (SRI) at Each Grade Crossing Location

Identifying Worst Crossing Locations (Black Spots of Accidents)

Figure 3.4: Flow Diagram for Identifying Black-Spots within Grade Crossings

Since the scope of this study is limited to analysis of predicted collision risk at

individual public grade crossings, the analysis presented here does not consider the

occurrence of "near misses" since they are not normally reported in the occurrence

data. Near misses represent breaches in safety that does not result in actual collisions.

3.2.1.4 Grade Crossing Accidents Data for Analysis

This research analyses the factors which influence safety effects of crossings using

Rail Grade Crossing accident and inventory data and information, obtained from

Federal Railroad Administration (FRA), Department of Transportation (DOT) United

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States. The main reasons for using data and information from USA level crossings

accident and inventory databases for the purpose developing risk assessment models

include:

• Easy and quick access to the data and information (both level crossing

accidents statistics and inventory information) through public access from the

FRA-DOT web-site;

• Exceptionally large sample size of grade crossing safety data (both inventory

and accidents information) in the USA compared with other countries, which

is good for model development and validation purposes. In this case, selected

databases from the USA consist of the highest number of annual average

collisions (3,081) and fatalities (368), making the highest number (241,817)

of railway-highway grade crossings compared to those of other countries in

the world.

• Experiencing great difficulty in obtaining the exact format and complete data

on level crossing accidents in Australia at the time of this analysis conducted.

In particular, the inventory information (crossing characteristics such as

highway traffic exposure, train movement, train speed, highway speed,

number of tracks, number of traffic lanes and track crossing angle, etc.) at

crossings is neither available nor accessible to the public. This means that

applicability of the model developed could be limited to certain sectors of

Australian environment.

3.2.2 Major Factors Influencing Accident Risks at Grade

Crossings

Risk factors refer to crossing attributes that explain variation in risk including the

expected number of collisions and their consequences. A risk factor can be a

combination of number of independent variables which affect the prediction of

accident risk. There are several such variables mentioned and included in developing

the earlier models for predicting collisions and their consequences (Saccomanno, Fu

& Miranda 2004). In this research, six major types of risk factors are identified

namely Crossing characteristics, Railway characteristics, Highway characteristics,

Vehicle attributes Driver attributes and Environmental attributes. A schematic view

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of these factors and associated variables that explain the collision risks at grade

crossings is shown in Figure 3.5. The factors and variables shown in Figure 3.5 are

discussed in greater detail below.

 

 

 

Accident Risk Factors

Railway Characteristics • Number of Trains • Number of Tracks • Train Speed • Type of Train

Highway Characteristics • Volume of Traffic • Surface Width • Type of Surface • Number of Lanes • Vehicle Speed

Environmental Attributes• View Factors • Adjacent Land Uses • Weather Effects • Visibility • Sun Glare

Driver Attributes • Decision making • Reaction Time • Observation • Awareness • Behaviour

Vehicle Attributes • Type of Vehicle • Breaking Performance • Accelerating

Performance • Size of Vehicle • Weight of Vehicle

Crossings Characteristics • Type of Crossing • Position of Crossing • Type of Protection • Crossing Angle of Track

Figure 3.5: Model of Accident Risk Factors and Associated Variables at Grade Crossings

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3.2.2.1 Crossings Characteristics

Type of Crossing: Three types of railway-highway crossings are generally

classified, namely; Public, Private and Pedestrian crossings.

Position of Crossing: Three positions of railway-highway crossings are generally

classified, namely; Railroad-Under, Railroad-Over and At Grade crossings.

Type of Protection: The type of protection has a significant effect on risk at grade

crossings (Farr, E.H., 1987). In general, there are two major types of protection

known as ‘Passive’ and ‘Active’. In this study, these two groups have been further

categorised in to two more sub-groups in each as shown in below.

• Passive

No Signs or No signals

Stop Signs or Cross-bucks

• Active

Signals, Bells or Warning Devices

Gates or Full Barrier

Passive traffic control systems consist of no signs, no signals, pavement markings,

grade crossing illumination, identifying and directing attention to the location of a

grade crossing, stop signs or cross-bucks. Passive devices themselves provide no

information to motorists on whether a train is actually approaching. Instead, crossing

users, upon being notified that they are entering a grade crossing, have to determine

for themselves whether a train is approaching and if it is safe to cross the tracks.

Active traffic control systems provide crossing users with a message that a train is

approaching the crossing. The user must surmise as to where the train could be with

respect to the crossing When a train is detected, typically some form of track

circuitry activates the warning device at the grade crossing, such as flashing light

signals and bells, full barriers or automatic gates.

Track crossing angle: Track angle refers to an intersection angle between the

roadway and track. The convention is to report this angle with respect to a

perpendicular line to the track at its intersection with the roadway centre line.

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3.2.2.2 Railway Characteristics

Number of tracks: Tracks are categorised into several classes (single main line,

double main line, siding, switching, etc). Mainline tracks usually carry through train

movement, while other tracks serve switching movements or terminal movements.

The number of tracks affects collision frequency and consequence.

Train speed: In the US Department of Transportation (USDOT) models, train speed

was found to affect both collision frequency and consequence. Consequently, an

increase in train speed results in an increase in collision severity.

Number of trains daily: Trains are classified as through trains (freight train and

passenger train) and switch trains. The train characteristics, such as train length,

weight, braking system, speed, and number of daily trains, influence the safety at

railway-highway grade crossings. The number of daily through trains was also found

to affect collision frequency in the USDOT model, in addition to considering train

exposure as one variable for both collision frequency and consequence models.

3.2.2.3 Highway Characteristics

Previous research has highlighted a number of highway characteristics affecting

collisions at grade crossings. These include traffic volume on roads, vehicle speed,

road surface type and width, number of lanes, etc. This section summarises the main

findings on the effects of highway characteristics on grade crossing collisions.

Traffic volume: Traffic volume on an intersected highway of a grade crossing has

obvious impact on the collision risk. The more traffic volume on highway, the more

vehicles are exposed to conflicts with train movements, the greater the probability of

collision. Previous grade crossings collision studies (Coleman & Stewart 1976; Farr

1987) have used the traffic volume as one of the important variables in their collision

prediction models. Traffic volume is expressed in terms of the Average Annual Daily

Traffic volume (AADT).

Surface width: Surface width affects vehicle-train collisions as well as vehicle-

vehicle collisions. Width can be used to reflect the number of lanes. An increase in

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the number of traffic lanes translates into higher traffic volume on the grade crossing

and greater chances for collisions. In addition, driver visibility usually decreases as

traffic at a grade crossing increases. Crossing surface width refers to the width of the

highway in metres plus shoulders (0.5 metres on each side) as measured at the

crossing approach.

3.2.2.4 Vehicle Attributes

Railway-highway grade crossings are exposed to diverse vehicles, from motorcycles

to tractor-trailers. These vehicles have contrasting characteristics that directly

influence safety at grade crossings. Equally important is the cargo these vehicles

carry, such as children in school buses and dangerous goods in trucks. Vehicle speed,

size and weight, accelerating and braking performances are important attributes

affecting the risk at grade crossings. On average, heavy trucks are involved in 16%

of all crossing collisions.

3.2.2.5 Driver Attributes

Driver attributes are a key component to explaining the occurrence of railway-

highway grade crossing collisions. Drivers’ decision and reaction time, as well as

their ability to judge train speed and observe multiple events at once, are all

important factors. At passive crossings, driver error and misperception may lead to

collisions. Active crossings can reduce recognition errors, but produce other forms of

driving behaviour error.

3.2.2.6 Environmental Attributes

Weather (e.g. rain, snow, fog) plays an important role when assessing the risk at

grade crossings. Other factors such as view, visibility, adjacent land uses and sun

glare for train and vehicle drivers also significantly influence safety at the crossings.

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3.3 Overview of Current Statistical Models for Predicting

Accidents and Consequences at Grade Crossings

Statistical models are generally used to examine the relationships between highway

accidents and features of highways. There were two major kinds of accident

prediction models developed and used by several researchers (as seen below) for

road safety evaluation:

• Linear Regression (LR) method; and

• Generalised Linear Modelling (GLM) approach to Poisson / Negative Binomial /

Gamma models.

Linear Regression (LR) method: The relationships between road vehicle accidents

and geometric design of road intersections such as horizontal curvature, vertical

grade, lane width, and shoulder width have been extensively studied earlier using

regression models (Oh et al. 2003; Ivan, Wang & Bernardo 2000; Abbess, Jarrett &

Wright 1983; Persaud & Dzbik 1993; Lyon et al. 2003; Miaou & Lord 2003;

Kulmala 1995; Poch & Mannering 1996). Even though these authors developed

vehicle collision prediction models using Linear Regression, several researchers (e.g.

Hauer, Ng & Lovell 1988; Jovanis & Chang 1986; Saccomanno & Buyco 1988;

Miaou & Lum 1993) showed that Linear Regression models lack the distributional

property to adequately describe collisions, as accidents are random variables with

non-normal distribution structure. This inadequacy is due to the random, discrete,

non-negative and typically sporadic nature that characterises the occurrence of a

vehicle collision. De Leur & Sayed (2001, p.806) stated that GLM approach has the

advantage of overcoming these shortcomings associated with LR models.

Generalised Linear Modelling (GLM) approach: Many past studies illuminating

the numerous problems with LR models (Joshua & Garber 1990; Miaou & Lum

1993) have led to the adoption of more appropriate regression models such as:

(i) Poisson regression model which is used to model data that are Poisson

distributed; and

(ii) Negative binomial (NB) model which is used to model data that have gamma

distributed Poisson means across crash sites allowing for additional

dispersion (variance) of the crash data.

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Although the Poisson and NB regression models possess desirable distributional

properties to describe motor vehicle accidents, these models are not without

limitations. One problem that often arises with crash data is the problem of ‘excess’

zeros which often leads to dispersion above that described by even the negative

binomial model (Lord, Washington & Ivan 2004; Washington, Karlaftis &

Mannering 2004). ‘Excess’ does not mean ‘too many’ in the absolute sense, it is a

relative comparison that merely suggests that the Poisson and/or negative binomial

distributions predict fewer zeros than present in the data. As discussed in the paper,

the observance of a preponderance of zero crashes results from low exposure (i.e.

train frequency and/or traffic volumes), high heterogeneity in crashes, observation

periods (that are relatively small), and/or under-reporting of crashes, and not

necessarily a ‘dual state’ process which underlies the ‘zero-inflated’ model (Lord,

Washington & Ivan 2004, p.7).

Thus, the motivation to fit zero-inflated probability models accounting for excess

zeros often arises from the need to find better fitting models which from a statistical

standpoint is justified. Unfortunately, however, the zero-inflated model comes also

with “excess theoretical baggage” that lacks theoretical appeal (Lord, Washington &

Ivan 2004). Another problem not often observed with crash data is under-dispersion

where the variance of the data is less than the expected variance under an assumed

probability model (e.g. the Poisson). One manifestation might be “too few zeros”,

but this is not a formal description. Under-dispersion is a phenomenon which has

been less convenient to model directly than over-dispersion mainly because it is less

commonly observed (Oh et al. 2006, p.347). Winkelmann’s gamma probability count

model offers an approach for modeling under-dispersed count data, and therefore

may offer an alternative to the zero-inflated family of models for modeling over-

dispersed data as well as provide a tool for modeling under-dispersion (Winkelmann

& Zimmermann 1995). It can therefore be concluded that in this study to utilise

GLM approach should be used for non-normal accident distribution.

3.3.1 Review on Common Models Predicting Highway Accidents

Currently, accident prediction models constitute the primary tools for estimating road

safety. There are different regression techniques to develop accident prediction

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models. The model development and subsequently the model results are strongly

affected by the choice of the regression technique used. Considerable research has

been carried out over the last two decades on developing different types of models

for predicting road collisions. The main focus of this work has been to establish

statistical links between predicted collisions and various roads geometric, traffic and

exposure attributes. Early prediction models adopted simple multivariate linear

regression techniques to establish a relationship between road geometry, traffic

characteristics and accidents (Miaou 1993). However, multivariate linear regression

failed to yield good results, since the underlying relationship proved to be essentially

non-linear.

A number of researchers adopted Generalized Linear Models (GLM) in predicting

road collisions (Hauer & Persaud 1987; Saccomanno & Buyco 1988). The

underlying probability distribution in these GLM models is either Poisson or

Negative Binomial. Poisson models attempted to capture the discrete, nonnegative

and somewhat rare nature of collisions. Maximum likelihood techniques are used to

obtain best-fit model parameters. In these models, the expected number of collisions

is expressed as a linear function of selected explanatory factors at a given location.

One of the limitations of Poisson models is that the mean (expected number of

collisions) is assumed to be equal to its variance. Recent research on road collision

prediction however has shown that, depending on the observed data, this assertion is

not always valid and must be investigated for different databases. In some databases,

historical collisions deviate considerably from the mean equal to variance

assumption inherent in the Poisson expression, and this could introduce significant

prediction error in the model results.

In many road collision databases, the variance in collision frequency is normally

higher than the mean, indicating a lack of explanation in the underlying Poisson

model (Lord, Washington & Ivan 2004; Ivan, Wang & Bernardo 2000). This is

referred to as Poisson over-dispersion. Poisson over-dispersion in road collision data

has been addressed by a number of researchers in recent years. Miaou (1993)

recommends using a more flexible Negative Binomial model to overcome the over-

dispersion problem in the historical data. Bonneson and McCoy (1993) and Daniel,

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Tsai & Chien (2002) reached similar conclusions that the Negative Binomial model

can overcome much of the over-dispersion error associated with Poisson models.

3.3.1.1 Poisson Regression Models

Integer count data are often approximated well by the Poisson distribution (Oh et al.

2006, p.349). In the Poisson regression model, the expected number of crashes

follows a Poisson distribution, where the expected crash count for the thi crossing iy

with N parameters is a function of covariates ijX with M parameters (i = 1,2,3,…..,N

and j = 1,2,3,…..,M ) so that:

)(~ ii Poissony λ (3.7)

where the link function in Poisson models is defined as:

)........(^

2211 iMMii XXX

i eβββλ +++=

(3.8)

or

)(^1

∑= =

M

j

ijj X

i eβλ

(3.9)

where the jβ ’s are estimated regression coefficients across covariates j = 1,2,3,…..,M

(for the slope intercept model the first covariate is a vector of 1’s) averaged across

crossings i = 1,2,3,…..,N. Because the Poisson regression model is heteroscedastic,

the model coefficients for equation 3.7 are typically estimated via maximum

likelihood methods. The likelihood function for the Poisson regression model

(equation 3.7) is given by:

∏ −=i i

yXe

y

eeL

iijjijXj

!

]][[)(

ββ

β (3.10)

If the mean of the crash counts is not equal to the variance (after accommodating a

reasonable degree of sampling variability), then the data are said to be either over-

dispersed or under-dispersed. In practice, over-dispersion is the most commonly

observed condition (variance>>mean) with respect to crash data, where the extra

variation is thought to arise from unobserved differences across sites (Washington,

Karlaftis & Mannering 2004; Lord, Washington & Ivan 2004).

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3.3.1.2 Negative Binomial Regression Models

The Negative binomial regression is a commonly applied alternative statistical model

to deal with over dispersed data (Oh et al. 2006, p.349). The negative binomial

model takes the relationship between the expected number of accidents occurring at

the thi crossing with N parameters and the function of covariates ijX with M

parameters (i = 1,2,3,…..,N and j = 1,2,3,…..,M ) as follows:

)(~ ii Poissony λ (3.11)

where the link function in NB models is defined as

)........( 2211 iiMMii XXX

i eεβββλ ++++= (3.12)

or

)()( 1*

∑= =

M

jiijj

i

X

i eeβελ

(3.13)

where the jβ ’s are estimated regression coefficients and the i

ε is the error term. In this

model, )( ieε is distributed as gamma with mean 1 and variance 2α . The negative

binomial distribution arises as a consequence of gamma heterogeneity in Poisson

means, hence the name. The effect of the error term in the negative binomial

regression model allows for over dispersion of the variance, such that:

( ) ( ) ( )2iii yEyEyVar α+= (3.14)

where α is the over dispersion parameter. If over dispersion, α equals 0, the

negative binomial reduces to the Poisson model. The larger the value of α , the more

variability there is in the data over and above that associated with the mean iλ . As is

the case for the Poisson regression model, the coefficients j

β are estimated by

maximizing the log likelihood )]([ βLLoge .

3.3.1.3 Gamma Models

Under-dispersion (when the crash mean is greater than the crash variance) is a

phenomenon which has been much less convenient to model directly. The gamma

model proposed by Winkelmann and Zimmermann (1995) provides an approach for

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count data with under or over-dispersion. More detailed discussion can also be found

in Cameron and Trivedi (1998). The gamma probability model for data is given by:

),(),()(Pr iii jGammajGammajy λααλα +−== (3.15)

where the link function in Gamma models is defined as:

)(1

∑= =

M

j

ijj X

i eβλ

(3.16)

0,1),( == jifjGamma iλα (3.17)

or

…)1,2,3… = (j 0 > j if,)(

1),(

0

)1( dueuj

jGamma uj

i

i −−∫Γ= λ ααλα (3.18)

The dispersion parameter is again α (there is under-dispersion if 1>α , over-

dispersion if 1<α and equi-dispersion if 1=α ), which reduces the gamma

probability to the Poisson model. Due to the relative scarcity of the gamma

probability count model in the transportation literature, additional model details are

provided. The conditional mean function for given bivariate ( iX ) is given by:

( ) ∑∞

==

1

),Gamma( j|j

iii jXyE λα (3.19)

and the cumulative distribution function is:

( ) 0,0)(

)(,|

0

)1( >>Γ= −−∫ i

uT

jj

i

i dueuj

TF i λααλλα λαα

.……0,1,2, = j)(

10

)1( dueuj

uT

ji −−∫Γ= λ αα

),Gamma( Tj iλα= (3.20)

3.3.1.4 Zero-Inflated Poisson Models

Zero altered count models, such as the zero-inflated Poisson (ZIP) and zero-inflated

Negative binomial (ZINB) models have seen recent attention in crash analysis

literature (Miaou 1993; Shankar, Milton & Mannering 1997). However, as pointed

out in Washington, Karlaftis and Mannering (2004) and with greater emphasis in

Lord, Washington and Ivan (2004), zero-inflated models may offer improved fit and

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perhaps better predictive performance, but these models lack theoretical appeal with

respect to crash data in most circumstances (Oh et al. 2006, p.351). So, if statistical

fit is the main objective of modelling, then zero-inflated models can often outperform

Poisson and negative binomial models. However, if agreement with underlying

model theory is paramount (in addition to statistical fit), then alternatives might be

sought. Zero-inflated models are theorised to account for “excess zeros”- zeros

observed in the data above and beyond the number of zeros predicted by Poisson or

negative binomial models.

A troubling assumption (of the zero-inflated theory with respect to crash data) is that

excess zeros may be present because certain crash locations can be considered to be

virtually safe in a zero accident state. Lord, Washington and Ivan (2004) demonstrate

that the excess zeros are not likely to be caused by an underlying zero state but

instead by high heterogeneity in crash counts, low exposure, or small spatial or

temporal measurement scales. The remaining ‘non-zero’ locations are theorised to

follow a normal count process for accident frequency in which non-negative integers

(i.e., including zero) are possible accident frequency outcomes over a specified time

period. The zip models can be thought of as two-stage models, where the first stage

is a splitting model (e.g. binomial) between two states (zero or count), and the second

stage is the count model (Poisson). The Zero-Inflated Poisson (ZIP) assumes that the

events, ),....,,( 21 nYYYY = are independent and

ieppY iii

λ−−+= )1(y probabilitwith 0 (3.21)

,.......2,1!

)()1(y probabilitwith =−= −

yy

epyY

y

i

i

ii

λλ

(3.22)

To test the goodness of fit of a zero-inflated model, Vuong (1989) proposed the

following test statistic for non-nested models:

])/(

)/([

2

1

ii

iii

xyf

xyfLogm =

(3.23)

where )/(1 ii xyf is the probability density function of the zero-inflated model and

)/(2 ii xyf is the probability density function of the Poisson or negative binomial

distribution. Then Vuong’s statistic (ν ) for testing the non-nested hypothesis of

zero-inflated model versus traditional model is (Greene 1997):

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mn

i

i

n

i

i

S

mn

mmn

mnn

v][

)()/1(

])/1[(

2

1

1 =−

= ∑∑

=

=

(3.24)

where m is the mean, mS is standard deviation, and n is a sample size.

3.3.1.5 Empirical Bayesian Model

Hauer and Persaud (1987) suggested that using an Empirical Bayesian (EB) approach

adjusts Poisson model estimates externally by historical collision experience. The EB

model can be viewed as a parallel approach to the Negative Binomial model rather

than its replacement. The EB model has been discussed extensively in the literature

to predict most types of rare events. Saccomanno et al. (2001) and Persaud (1990)

have used EB models to designate highway black-spots.

3.3.2 Overview on Existing Mode ls Developed for Prediction of

Collisions at Railway-Highway Interfaces

This section provides an overview of existing models for predicting accident risk and

identifying black-spots at railway-highway grade crossings in countries such as the

United States and Canada. Accident risk includes both the expected number of

collisions (frequency) and their consequent damages (severity). The discussion

highlights a number of independent factors that are instrumental in explaining

variations in collision frequency and consequence at individual grade crossings. It

also reviews several representative studies that have attempted to identify black-spots

for both Road and Rail sectors.

Because of the lack of detailed information on crossing element data and the failure

of selecting appropriate tools for analysing the data, statistical models explaining the

relationships between roadway geometry, grade crossing characteristics, and crossing

accident frequencies have rarely been developed. Therefore, research gaps remained

regarding the identification of factors associated with crashes at railway-highway

crossings. In this context, Oh et al. (2006) have provided some useful knowledge on

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complex relationships between crashes involving motor vehicles and/or trains

through the application of statistical models using crash data. The contrasts and

tradeoffs between various probability models are discussed, emphasizing on the

greatest insight into railway-highway crossings related crashes. Safety levels at

highway-rail crossings continue to be of major concern despite of improved design

and application practices. This suggests the need to re-examine both accident

prediction methods and application practices at railway-highway crossings. Based on

a comprehensive review of previously developed accident prediction methods, it is

noted that the Peabody Dimmick Formula, the New Hampshire Index and the

National Cooperative Highway Research Program (NCHRP) Hazard Index lack

descriptive capabilities due to their limited number of explanatory variables. The US

Department of Transportation’s (USDOT) Accident Prediction Formula, which is

most widely used, also has limitations related to the complexity of the three-stage

formula and its decline in accident prediction model accuracy over time.

Over the past several decades, a number of collision frequency models have been

developed. These models generally have taken one of two basic perspectives:

absolute and/or relative risk. Absolute models yield the “expected number of

collisions” at a given crossing for a given period of time. Relative models, on the

other hand, yield a “hazard index”, that represents the relative risk (frequency and/or

consequence) of one crossing compared to another. Among many models, models

developed by Coleman and Stewart (1976) and Farr (1987) are found to be typical

absolute collision prediction models. The USDOT model is generally recognised as

being the industry standard for collision risk prediction at railway-highway grade

crossings. It is noted from the literature that there are many relative hazard index

models developed in the United States between 1950 to 1970, including the

Mississippi Formula (1970), the New Hampshire Formula (1971), the Ohio Method

(1959), the Wisconsin Method (1974), Contra Costa County Method (1969), the

Oregon Method (1956), the North Dakota Rating System (1965), the Idaho Formula

(1964), the Utah Formula (1971), and the City of Detroit Formula (1971). In this

section, four representative “relative risk” models (New Hampshire (1971), NCHRP

50 Hazard Index (1964), Ohio (1959) and City of Detroit (1971) and three

representative “absolute risk” models (Coleman & Stewart 1976; Farr 1987) are

discussed in details.

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3.3.2.1 Relative Risk Models

Relative risk (hazard index) models are not generally used to justify intervention

because they do not provide objective estimates of the risks needed to justify this

intervention on a cost-effective basis. Accordingly, relative risk models are of limited

use in black-spot identification and analysis.

(a) New Hampshire Index (1971)

The New Hampshire Index was another evolutionary step in predicting accident

models at grade crossings (Austin & Carson 2002). This Index is as follows:

fPTVHI **= (3.25)

where:

HI - Hazard Index;

V - Average annual daily traffic (AADT);

T - Average daily train traffic; and

fP - Protection factor (indicative of warning devices present).

In comparison with the Peabody Dimmick Formula, it is noted that this method uses

the same variables in predicting railway-highway crossing accidents. However, the

value of protection factor varies from state to state and this issue raises concern over

the model’s validity in predicting accidents accurately. Some states in the USA

modified this index by including other factors such as train speed, highway speed,

number of tracks, etc.

(b) NCHRP 50 Hazard Index (1964)

With a joint effort between the American Association of State Highway Officials and

the Association of American Railroads (AAR), the National Cooperative Highway

Research Program (NCHRP) Hazard Index was developed in 1964 (Austin & Carson

2002). The NCHRP 50 Hazard Index can be expressed as a complex formula or

reduced to a more simple equation of coefficients that are taken from a few tables

and graphs, which are provided in the NCHRP Report 50 (Schoppert & Hoyt 1968).

The simple formula for calculating the expected number of accidents per year is

given by:

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(CTD)* B *A =EA (3.26)

where;

EA - Expected accident frequency;

A - Vehicles per day factor provided in tabular format based on 10 years ADT figure;

B - Protection factor indicative of warning devices present; and

CTD - Current trains per day

The NCHRP Report 50 also provides formulae for estimating the number of non-

train involved accidents per year as follows:

For Automatic gates:

(ADT) * 0.00036 + 0.00866 = X (3.27)

or

(ADT)/100 * X =EA (3.28)

For other traffic control devices:

(ADT) * 0.00036 + 0.00499 = X (3.29)

or

(ADT)/100 * X =EA (3.30)

where;

EA - Expected number of accidents per year;

X - Probability of coincidental vehicle and train arrival scaled by 310− ;

ADT - Average daily traffic

This Index clearly resembles the basic formula for the New Hampshire Index. The

NCHRP program provides information for the installation of automatic warning

devices at crossings on a statewide basis according to a hazard index which is

calculated using ADT, number of train movements, latest 5-year accident experience,

and a protection factor based on the type of existing warning devices at the crossing.

Based on the program, the DOT in the state of Connecticut designs and constructs

between five and six crossings per year (Federal Railroad Administration 1996).

Since the start of the program, 120 crossings have received safety improvements.

(c) Ohio formula (1959)

The Ohio model is expressed as:

SDR + + + + + = H.I fffff NLGBA (3.31)

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where:

H.I - Hazard index

fA - Collision probability factor

fB - Train speed factor

fG - Approach gradient factor

fL - Angle of crossing factor

fN - Number of tracks factor

SDR - Sight distance rating

(d) City of Detroit formula (1971)

The City of Detroit model is of the form:

2 + %} - (100% ] + + +SDR * 30

+ 20

+ 10

[ 1000 = H.I effff APRXN

SFPT

(3.32)

where:

T - Average 24 hour train volume

P - Number of passenger trains in 24 hours

F - Number of freight trains in 24 hours

S - Number of switch trains in 24 hours

fN - Number of tracks factor

fX - Condition of crossing factor

fR - Road approach factor

fP - Protection factor

eA - Collision occurrence

SDR - Sight distance rating

3.3.2.2 Absolute Risk Models

(a) Peabody Dimmick Formula (1941)

This formula was one of the earliest railway-highway crossing accident prediction

models. It was developed in 1941 using five year accident data from 3,563 rural

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railway-highway crossings in 29 states in the US. The Peabody Dimmick formula is

primarily used to determine the expected number of accidents at railway-highway

crossings in five years period and is given by:

K + *

1.28 =171.0

151.0170.0

5P

TVA

(3.33)

where:

5A - Expected number of accidents in 5 years;

V - Average annual daily traffic (AADT);

T - Average daily train traffic;

P - Protection coefficient (indicative of warning devices present); and

K - Additional parameter (determined from the graph of unbalanced accident factor)

The Peabody Dimmick Formula is derived from a stochastic model where V * T

represents the interaction of motor vehicle traffic and trains. The coefficients were

derived from a data fitting procedure where the data used is considerably old.

(b) USDOT Accident Prediction Equations (1980)

The US Department of Transportation (USDOT) accident formula was developed in

the early 1980s to address earlier model limitations and used to assist in the

assessment of grade crossing hazards (Austin & Carson 2002). This formula

combines two independent calculations to estimate an accident prediction value. It

consists of a basic equation which predicts the number of crossing collisions and

equations that predict the probabilities that collisions will result in fatality or

personal injuries. The basic USDOT accident prediction equations consist of three

sets of equations that are used for each of the three categories of traffic control

devices as follows:

• Passive;

• Flashing lights; and

• Automatic gates.

The three equations generally utilise two highway, three railroad and two

combination railway-highway factors. Various other collision prediction or hazard

index formulas utilise greater or fewer numbers of factors, many that are identical or

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similar to the USDOT equation factors. It may be noted that the results of the various

formulae, when applied to a group of crossings, generally rank crossings in the same

order though the predicted number of collisions or hazard index at a particular grade

crossing differs. The Federal Highway Administration’s Railroad-Highway Grade

Crossing Handbook provides information concerning some of the various formulas

(Federal Highway Administration 1986).

HL * HT * MS * HP * DT * MT * EI *K = a (3.34)

where:

a - Initial accident prediction at the crossing (accidents per year);

K - Formula constant;

EI - Factor for exposure index based on product of highway and train traffic;

MT - Factor for main tracks;

DT - Factor for number of through trains per day during daylight;

HP - Factor for highway paved (yes or no);

MS - Factor for maximum timetable train speed;

HT - Factor for highway type;

HL - Factor for highway lanes.

The USDOT equation factors are based on crossing characteristics that are identified

in the national crossing inventory database. The basic two USDOT equation highway

factors are based on the number of highway lanes and whether or not the highway is

paved (a third highway factor, the type of highway: urban or rural arterial, collector,

local road, etc. was removed from the equation when it was updated in 1987). The

three railroad factors are based on the number of main tracks, number of daylight

through trains per day, and the maximum authorised timetable train speed. The two

combination railroad-highway factors are the types of warning device (passive,

flashing lights, or automatic gates), and exposure index. The exposure index in turn

is based on the product of the annual average number of highway vehicles per day

(AADT) and the average total number of train movements per day. The full USDOT

formula includes an adjustment based on recent collision experience, typically the

most recent 5-year period for which complete collision information is available. The

numeric value of each of these factors is calculated using the relationship given in

Table 3.5. The final accident prediction formula is expressed as:

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)/()(

)()( 00

0 TNTT

Ta

TT

TA +++=

(3.35)

where:

A - Final accident prediction at the crossing (accidents per year);

a - Initial accident prediction at the crossing from basic formula (accidents per year);

(N / T) - Accident history prediction (accidents per year) where N is the number of

observed accidents in T years at the crossing.

Table 3.5: USDOT Accident Prediction Equations for Crossing Category by Crossing Characteristic Factors

Crossing

Category Crossing Characteristic Factors

K EI MT DT HP MS HT HL

Passive

0.002268

[c * t +

3334.0

2.0 ] / 0.2

)(2094.0 mt

e [d +

1336.0

2.0 ] / 0.2

)1(6160.0 −− hp

e

)(0077.0 ms

e

)1(1000.0 −− ht

e

1.0

Flashing

Lights

0.003646

[c * t +

2953.0

2.0 ] / 0.2

)(1088.0 mt

e [d +

0470.0

2.0 ] / 0.2

1.0 1.0 1.0 )1(1380.0 −hl

e

Automatic

Gates

0.001088

[c * t +

3116.0

2.0 ] / 0.2

)(2912.0 mt

e

1.0 1.0 1.0 1.0 )1(1036.0 −hl

e

Highway Type HT Value

c = Annual average vehicles per day Rural Interstate 1

t = Average total trains per day Other principal arterial 2

mt = Number of main tracks Minor arterial 3

d = Average number of through trains per day Major collector 4

hp = Highway paved (Yes=1, No=2) Minor collector 5

ms = Max timetable train speed (mph) Local 6

ht = Highway type factor value Urban Interstate 1

hl = Number of highway lanes Other freeway and expressway 2

Other principal arterial 3

Minor arterial 4

Collector 5

Local 6

(c) Coleman-Stewart model

The Coleman-Stewart model uses an expression of the form:

)( +)( + )( + = 23210 TLogCTLogCCLogCCHLog (3.36)

where:

C - Vehicle movements per day

T - Train movements per day

H - Average number of collisions per crossing per year

0C , 1C , 2C , 3C - Coefficients

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A series of collision frequency expressions were developed in the Coleman-Stewart

model for different track classes (number of tracks and region) and warning devices

(gates, flashing lights and signs). The values of relevant coefficients depend on type

of track and warning devices and they are summarised in Table 3.6.

Table 3.6: Coefficients of Coleman-Stewart Model

Category 0C 1C 2C 3C

Single-

track,

Urban

Automatic Gates -2.17 0.16 0.96 -0.35

Flashing Lights -2.85 0.37 0.16 -0.42

Cross bucks -2.38 0.26 0.78 0.18

Single-

track,

Rural

Automatic Gates -1.42 0.08 -0.15 -0.25

Flashing Lights -3.56 0.62 0.92 0.38

Cross bucks -2.77 0.4 0.89 -0.29

Multiple-

track,

Urban

Automatic Gates -2.58 0.23 1.3 0.42

Flashing Lights -2.5 0.36 0.68 -0.09

Cross bucks -2.49 0.32 0.63 -0.02

Multiple-

track,

Rural

Automatic Gates -1.63 0.22 -0.17 0.05

Flashing Lights -2.75 0.38 1.02 -0.36

Cross bucks -2.39 0.46 -0.5 0.53

3.3.3 Overview of Existing Models in Predicting Consequences of

Collisions at Railway-Highway Interfaces

A number of statistical methodologies for predicting road collision severity or

consequence have been documented. In a broad range of studies, Nassar,

Saccomanno and Shortreed (1994) proposed a series of sequential, nested logit

models to predict occupant injury severity for road collisions. Three classes of

explanatory factors were considered: physical (energy dissipation), driver condition

and action, and occupant passive response (e.g. wearing a seat belt, seating location

in vehicle). Since the Nassar model is occupant-specific, the severity of a given

collision requires the summation of the severity experienced by all occupants of all

vehicles involved. Some studies suggest using log-linear regression models rather

than logit models to predict road collision severity. It is argued that logit models do

not provide a systematic means of considering interactions among the various

independent risk factors. In this context, Abdel-Aty et al. (1999) adopts a log-linear

model to investigate the risk factors affecting bus driver injury severity, and finds

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significant interaction effects between collision fault, time of collision, and collision

type affected severity. It is noted that different levels of severity might be aggregated

into a single combined value, which can be linked with risk factors for predicting

overall collision consequence at a given location (or grade crossing).

3.3.3.1 USDOT Consequence Model (1987)

The USDOT collision consequence model for railway-highway grade crossings

considers two levels of severity namely fatalities and casualties (Farr, E.H., 1987).

Fatal collisions are defined as collisions that result in at least one fatality, while

casualty collisions are defined as collisions that result in either at least one fatality or

injury. Both types of collisions are reported in the Federal Railway Administration

(FRA) occurrence databases. As considered in the USDOT consequence model, fatal

collisions are a sub-set of casualty collisions. In the USDOT consequence model the

probability of a fatal collision (FA) given the prior occurrence of a collision (C) is

expressed as:

UR)* TS * TT * MS * KF (1

1 = C)|(FA P +

(3.37)

where:

KF = 440.9

MS =9981.0)( −ms

TT = 0872.0)1( −+tt

TS = 0872.0)1( +ts

UR = ure 3571.0

ms = Maximum timetable train speed

tt = Through trains per day

ts = Switch trains per day

ur = Urban rural crossing, 0 for rural and 1 for urban

The probability of a casualty collision (CA) given a collision is expressed as:

UR)*TK * MS * KC (1

1 = C)|(CA P +

(3.38)

where:

KC = 4.481

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MS = 343.0)( −ms

TK = tke 1153.0−

UR = ure 3571.0

tk = Total number of tracks

The expected number of fatal and casualty collisions per crossing was obtained by

multiplying the expected number of collisions by the conditional probability of a

fatal or casualty collision, such that:

C)|P(FA * E[C] = (FA) E (3.39)

and

C)|P(CA * E[C] = (CA) E (3.40)

It should be noted that USDOT consequence model does not take into account the

type of warning device found at a given crossing. Moreover, the model treats all fatal

collisions in a similar fashion regardless of number of fatalities incurred. The

USDOT consequence model focuses on the likelihood of a fatal and/or casualty

collision, not the numbers of fatalities or casualties associated with each collision.

This limits its use in distinguishing differences in severity among different collisions

at a grade crossing.

3.3.3.2 Canada - University of Waterloo Consequence Model (2003)

Department of Civil Engineering at University of Waterloo, Canada developed two

types of collision consequence models for grade crossings in 2003 as follows:

The Poisson Consequence model of the form is given by the equation of:

] *0253.0*0051.0TN*0.2433-PI * 0.0718 -0.4818[)|(

TSPDTACCqE e +++= (3.41)

The Negative Binomial Consequence model of the form is given by the equation of:

] *0250.0*0069.0TN*0.2262-PI * 0.3426[)|(

TSPDTACCqE e ++= (3.42)

where:

E(Cq | C) = Expected consequences per collision

PI = Number of persons involved

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TN = Number of railway tracks

TA = Track angle

TSPD = Maximum train speed (mph)

3.3.4 Overview of Existing Models in Predicting Overall Safety

Risks at Railway-Highway Interfaces

It is noted from the literature that there are a few research studies on appropriate

statistical models to assess the overall safety risks at grade crossings. Among those

research studies, Saccomanno et al. (2003)’s work is significant in the development

of risk assessment model and presents an appropriate risk model for targeting black-

spot crossings in Canada. The model was generated with appropriate grade crossing

characteristics and validated with several statistical techniques. However, in their

approach, accidents frequency and accidental consequences were considered as of

equal importance in the model development and thus assigned the same value. In this

research study, an improved quantitative risk assessment approach is being

developed, addressing those limitations outlined above where the two key indicators

(accidents frequency and accidental consequences) are combined together to provide

a single risk measure (Safety Risk Index).

3.4 Evaluation of Risk at Grade Crossings with Application of

Safety Risk Index (SRI)

In general, evaluation of risk at grade crossings is carried out using a quantitative

safety risk. A quantitative safety risk at a grade crossing is described as combination

of the magnitude of potential accidental consequences and the likelihood that those

accidents may occur. The scales to describe the magnitude of potential can be

adapted or adjusted to suit the circumstances of accidents. In fact, different

descriptions may be used for different risks. As such, Safety Risk Matrix method for

risk analysis is considered where it simply divides the identified risk regions into

four categories (low, medium, high and extremely high risks) as shown in Figure 3.6.

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Figure 3.6: Graphical Model of a Typical Quantitative Safety Risk Matrix

3.4.1 Identifying Worst Accident Crossing Locations (Black-Spots)

Safety levels at railway-highway crossing locations continue to be a major concern

for both the rail and highway authorities in many countries worldwide. Black-spots

are defined as crossings with unacceptably high-expected risks (frequency and/or

consequence). It is noted that a number of systematic safety improvement programs

for railway-highway crossings rely on appropriate models. These models can be used

to identify those black-spots where the risk is extremely high and safety

countermeasures are warranted. Based on current approaches and associated models,

the procedure for identifying black-spots adopted in this study is illustrated in

Figure 3.7. This procedure consists of five related components:

• Predict the number of accidents per each location;

• Estimate consequence or severity per an accident at each location;

• Compute the Safety Risk Index (SRI) using both predictions for accidents and

consequences;

• Set up thresholds based on available resources; and

• Identify black-spots for safety intervention.

Extremely High Safety Risk

High Safety Risk

Accidental

Consequences

Medium Safety Risk

Low Safety Risk

Frequency of Accidents

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Figure 3.7: Flow Diagram for Procedures of Identifying Black-Spots

3.4.2 Developing an Improved Quantitative Method for Black-

Spots Identification with Application of SRI

In this research study, higher risk potential grade crossings (black-spots) are

identified using a graphical method, based on a two-dimensional risk prescription for

comparing predicted frequencies and consequences to established risk thresholds. An

example of such graphical representation is shown in Figure 3.8.

Predicting Accidents for All Public Grade Crossings

Estimating Severity per an Accident at Each Public Grade Crossing

Traffic Exposure

Calculating Safety Risk Index (SRI) at Each Grade Crossing Location

Drawing Two Dimensional Safety Risk Index Graph to Represent the Risk at Each Grade Crossing Location and

Setting up a Threshold Curve

Identifying Dangerous Accidental Locations

(Black Spots of Accidents)

Frequency of Accidents

Accidental Consequences

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Black Spot Identification

0

0.5

1

1.5

2

2.5

3

0 0.2 0.4 0.6 0.8 1 1.2

Expected Accident Frequency

Est

imat

ed E

quiv

alen

t Fat

aliti

es

Safety Risk Index Threshold Curve (X*Y = oℜ )

X

Y

A (X,Y)

Figure 3.8: Identifying Black-Spots within Grade Crossings Based on Safety Risk Index

In this case, the x-axis represents the potential for accidents at a given crossing (long

term likelihood for collisions) over a given period of time, while the y-axis shows the

expected accidental consequences per accident in terms of equivalent fatalities

(combination of fatalities, injuries and property damage). Each point on the graph

represents the status of safety risk at relevant crossing. For example, point ‘A’ on the

graph represents a grade crossing (say ‘C’) with estimated accidents of X and

estimated consequences of Y. By definition, Safety Risk Index (ℜ ) for the

crossing ‘C’ is defined as the product values of both accidents (X) and

consequences (Y) estimated for the crossing. i.e.:

esConsequenc Estimated * Accidents EstimatedIndex Risk Safety = (3.43)

or

Y*X=ℜ (3.44)

Mathematically if the value of either X or Y increases, then the value of ℜ will also

increase. That means that as we move the point ‘A’ away from the origin on the

graph along each axis, we will enter the area representing the crossings with higher

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risk potentials. If the point ‘A’ is moved away from x-axis, then it represents a

crossing with high estimated consequences. Conversely, if the point ‘A’ is moved

away from y-axis, then it represents a crossing with high estimated accidents. By

plotting points for each crossing on the graph for all four types of protection, the risk

pattern of all crossings can be depicted and black-spots are conveniently identified in

the relevant crossings protection type.

A key element in identifying black-spots is an objective definition of risk tolerance

or threshold that can be linked to various decision options. For example, if risk

exceeds a given threshold, a certain type of intervention would be considered. Risk

tolerance can be depicted as a safety risk index threshold curve superimposed on the

crossing risk estimates. The equation of the threshold curve is given as X.Y

= 0ℜ where 0ℜ is critical risk index value. The process of selecting threshold value

or critical risk index value ( 0ℜ ) is explained later in Chapter 6. Any crossing with

expected collision frequency and consequence that lies beyond the acceptable risk

thresholds would be designated as a black-spot. In Figure 3.8, crossings identified

over the safety risk index threshold (i.e. ℜ > 0ℜ ) would be considered high risk

(black-spots), such that some form of safety intervention would be justified even at

high cost. Crossings on or just around the SRI threshold (i.e. ℜ ≈0ℜ ) reflect

moderate risks, and intervention is justified if its cost does not exceed its potential

safety benefits. Crossings identified under the safety risk index threshold (i.e.

ℜ < 0ℜ ) would be considered acceptable, requiring no intervention.

3.5 Summary

In this chapter, the fundamental concepts for safety risk evaluation, some risk

evaluation techniques and types of analysis such as quantitative, qualitative and

semi-quantitative have been thoroughly discussed with appropriate examples. A

theoretical framework was initially established for safety risk evaluation at rail grade

crossings. A generic quantitative risk assessment model by the name of Safety Risk

Index (SRI) was then developed and its basic concepts were clearly discussed. An

illustrated example for application of SRI was demonstrated. The major steps to

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achieve objectives of this study were then identified. The source and the nature of

grade crossing accidents data for the analysis were discussed. Some major factors

and their variables influencing accident risks at grade crossings were modeled and

explained in greater details.

Several statistical models which are currently used for predicting highway accidents

were identified and discussed with their applications. Linear Regression (LR)

method and Generalized Linear Modeling (GLM) approach were identified as the

two major basic forms for modeling. The common models predicting highway

accidents with modeling techniques such as Poisson, Negative Binomial Regression,

Gamma, Zero-inflated Poisson and Empirical Bayesian were also reviewed. Some

existing models (Relative Risk and Absolute Risk Models) developed for prediction

of collisions, consequences and overall safety risks at railway-highway interfaces

were then overviewed.

As described and outlined above, various research methods have been used in

predicting accident frequencies and consequences in the context of USA and Canada

rail grade crossings. However, there are a few research studies on appropriate

statistical models to assess the overall safety risks at grade crossings. Among them,

Saccomanno et al. (2003)’s work is significant in the development of risk assessment

model and presents an appropriate risk model for targeting black-spot crossings in

Canada. However, accidents frequency and accidental consequences were considered

as of equal importance in their approach, assigning the same value for both

indicators. In this study, an improved quantitative method for evaluating risks at

grade crossings was finally developed with application of Safety Risk Index (SRI),

addressing those limitations where accidents frequency and accidental consequences

are combined together to provide a single risk measure. As stated earlier, this method

bridges some gaps identified in the development of earlier models. In particular, the

new approach assesses and prioritises risks at grade crossings where the two key

indicators (accidents frequency and consequences) are combined to provide a single

risk measure (Safety Risk Index).

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Chapter 4

Data Collection and Consolidation

4.0 Introduction

The previous chapter outlined the details of an improved quantitative method for

evaluating risks at grade crossings, using the application of Safety Risk Index (SRI).

Given it is the foundation for overall research methodology for developing and

testing models for improving safety at level crossings through assessment and

prioritising the risks, this chapter describes various aspects of data including source

of data, nature of databases, data extraction and analysis. Thus, data collection,

extraction and analysis are discussed in detail as the basis for developing and testing

the railway-highway grade crossing risk assessment models (including accidents and

consequences predictions).

The source of data is described with details of individual databases including

accessibility and data selection. In this case, the selection of particular country-

specific data is justified on the basis of the amount of data and public access. The

nature of data is described along with data consolidation. As part of data extraction,

explanatory variables (train speed, highway speed, number of tracks, number of

highway lanes, etc.) and factors (protection types used at crossings, highway

pavement status, crossing surface material, type of crossing, position of crossing,

etc.) used in the development of models are identified and described. A preliminary

data analysis on accidents and consequences at level crossings over a five-year

period is conducted for justification of the research’s major focus.

4.1 Source of Rail Crossing Accidents Data and Information

Given this research is focusing on safety risk assessment and analysing the safety

effects of factors associated with rail crossings, selection of data source with railway-

highway crossing accidents and inventory data (characteristics of railway crossings)

is primarily based on (i) the availability of large data set and (ii) details and

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information on wider range of variables and factors. Considering lack of adequate

and necessary data in the Australian context and public access to large amount of

data from US, the development of risk assessment models in this study is based on

the US grade crossings accidents data. Thus, data available from the United States

Department of Transportation Federal Railroad Administration (USDOT FRA) is

selected, as data covers a wider range of variables and factors; more reliable and

relevance information; richness and superiority data; is publicly available; and can be

easily accessed through the internet. For the purpose of this research, focusing on the

development of risk assessment models, data drawn from two major databases

(Safety Inventory database and Crossing Accidents database) of USDOT FRA over a

period of five years (2001-2005) are considered. The inventory database of railway

crossings contains static information such as highway and railway geometric

characteristics, traffic volumes and selected train and vehicle operating features, etc.

In the five-year period (2001-2005), the database shows 394,396 records of level

crossings. The crossing accidents database shows dynamic data or information on

collision occurrences and their consequences at those crossings for the same period.

Both databases share a common reference number that permits linkage of each

collision occurrence to crossings specified by a Crossing ID number. These two

databases (Safety Inventory and Crossing Accidents) are downloaded from the

USDOT FRA Railway-Highway crossing safety database websites:

(i) http://safetydata.fra.dot.gov/OfficeofSafety/publicsite/Downloaddbf.aspx; and

(ii) http://safetydata.fra.dot.gov/OfficeofSafety/publicsite/on_the_fly_download.aspx

4.1.1 Database of Railway-Hi ghway Crossings Data and

Information (Inventory Database)

Database of Railway-Highway Crossings Information refers to the USDOT FRA

inventory database. It provides a range of data and detailed information for

administration and management of grade crossings using statistical analysis. It

contains the static data and information on geometric characteristics of highways and

railways of each crossing, and traffic volume of both highways and trains across

entire railway-highway crossings in the USA.

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4.1.1.1 Attributes and Variables in Inventory Database

Data and information on 152 variables related to each crossing are available in the

inventory database as shown in the Table A1-1 in Appendix 1. However, most of the

variables are found to be having either:

• Incomplete or missing information; or

• Information reflecting another variable; or

• Information not relevant for the analysis.

Figure 4.1 depicts the distribution of these groups of variables among the variables

that were selected for initial modelling purposes. The highest percentage of variables

are found to be in the group which contains only a few records (35.5%) followed by

the group in which the variables have no obvious relevancy in making models

(31.6%) and then the group in which variables partially reflect others selected for

model predictions (25.7%). It seems that only the remaining 7.2% of variables are

suitable for initial selection.

Variables selected for models

7.2%

Part of another variable selected for

models25.7%

Not relevent for model prediction

31.6%

Only few records available in the

database35.5%

Distribution of selected and non-selected variables from inventory database

Figure 4.1: Distribution of Different Categories of Variables in the Inventory Database

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143

4.1.1.2 Selection of Appropriate Variables from Inventory Database

In this case, relevant variables are selected from the inventory database of mainly

geometric characteristics of railway crossings using non-statistical and statistical

methods. Non-statistical method is applied first, by considering and eliminating data

quality issues (such as duplicate or similar information, incomplete or missing data

and non-relevant information) apparent in the databases. Based on this method the

variables, which have extremely higher data quality issues, are discarded in the first

instance. Among the 152 variables identified in the inventory database, 54 are

eliminated due to the availability of only a few records; 48 are rejected for non-

relevance for model prediction; and 39 are discarded as they reflect another variable

selected for modelling prediction. A total of eleven (11) variables are finally selected

for the modelling analysis by non-statistical method. According to the model

illustrated for accident risk factors (refer to Figure 3.5), these eleven variables can be

grouped under three accident risk factors (i.e. Crossing characteristics, Railway

characteristics and Highway characteristics) as described in the previous chapter.

These variables, with some descriptive statistics under relevant accident risk factors,

are briefly discussed below. The following are the five variables belonging to the

accident risk factor related to crossing characteristics.

Crossing Locat ion Ident ificat ion (CROSSING): Each crossing in the database

has a Crossing ID, which indicates its location by street, city, county and state. The

selected data over a period of five years contains crossing information from the fifty

states of the USA. For example, Texas has the highest number of crossings (16,806)

followed by Illinois (13,111), California (12,450), Kansas (10,130) and so on.

Hawaii contains the least number of crossings (only 8) followed by Columbia

District (40).

Posit ion of Crossing (POSXING): This variable describes the position of

crossings. Three positions of railway-highway crossings are reported, namely:

• At Grade (350,399 crossings);

• Railroad-Under (22,643 crossings); and

• Railroad-Over (21,354 crossings).

However, this study is only concerned on ‘At Grade’ crossings.

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Type of Crossing (TYPEXING): This variable in the database describes the type of

crossings. Three types of railway-highway crossings are reported, namely:

• Public (249,054 crossings);

• Private (141,081 crossings); and

• Pedestrian (4,261 crossings).

However, this study is only concerned with ‘Public’ crossings.

Type of Warning Device at Crossing (WDCODE): This variable describes the

types of warning device at crossings. Nine types of warning (by maximum

protection) are cited in the database as:

Type 1: No signs or signals (83,418 crossings)

Type 2: Other signs or signals (1,414 crossings)

Type 3: Cross-bucks (107,050 crossings)

Type 4: Stop signs (17,970 crossings)

Type 5: Special active warning devices (5,996 crossings)

Type 6: Road traffic signals, wigwags, bells, or other activated (2,144 crossings)

Type 7: Flashing lights (31,972 crossings)

Type 8: All other gates (42,231 crossings)

Type 9: Four quad (full barrier) gates (439 crossings)

However, 101,762 crossings could not be grouped into one of the above-mentioned

types. It is recognised that Warning Types 1, 2, 3 and 4 show “Passive crossing”

(crossing without any kind of active warning indication of train approaching to road

users) groups and Types 5,6,7,8 and 9 indicate “Active crossing” (crossing with

some kind of active warning indication of train approaching to road users) groups.

For the purpose of simplification, all nine types of warning are categorised into four

main groups in this study (namely Protection Types 1, 2, 3 and 4) and defined as:

• Protection Type 1: No signs or no signals [Types 1 & 2 – 84,832 crossings]

• Protection Type 2: Stop signs or cross-bucks [Types 3 & 4 – 125,020

crossings]

• Protection Type 3: Warning devices or bells or flashing lights [Types 5, 6 &

7 – 40,112 crossings]

• Protection Type 4: Gates or full barriers [Types 8 & 9 – 42,670 crossings].

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Track Crossing Angle (XANGLE): Track crossing angle refers to the smallest

angle intersected between the track and highway. It is grouped into three categories

of data: (i) 0-29 degrees, (ii) 30-59 degrees, and (iii) 60-90 degrees.

The three variables within the accident risk factor related to railway characteristics

are:

Train Movement through Crossing (TOTALTRN): Train movement is expressed

in terms of the total number of daily trains (freight, passenger and switching trains)

through each crossing. Records vary in a range of 1 to 364 in the database.

Number of Main Tracks at Crossing (MAINTRK): In general, tracks are

categorised into several groups such as main tracks, siding tracks, switching tracks,

etc. As the main tracks usually carry through train movement while other tracks

serve terminal or switching movements, the number of main tracks is used for

modelling in this study. It varies from the range of 0 to 7 in the database.

Maximum Time Table Speed of Tr a ins at Crossing (MAXTTSPD): Train speed

at crossings is expressed in terms of the maximum scheduled time table speed in

mph. It varies from the range of 1 to 110 mph in the database.

The following are the three variables within the accident risk factor related to

highway characteristics.

Highw ay Traffic Volume through Crossing (AADT): Highway traffic volume is

expressed in terms of the Average Annual Daily Traffic (AADT) for the road

through each crossing. It varies from the range of 1 to 308,060 in the database.

Speed of Highw ay Vehic les at Crossing (HWYSPEED): Highway speed at

crossings is expressed in terms of the posted vehicle speed limit in mph. It varies

from the range of 1 to 80 mph in the database.

Number of Traffic Lanes at Crossing (TRAFICLN): Number of traffic lanes

refers the total number of highway lanes, which cross the rail tracks at crossings. It

varies from the range of 0 (zero means pedestrian crossing) to 9 in the database.

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Table 4.1: Filtering Process in Selecting Appropriate Variables from Inventory Database

Name of database

where variables

are obtained

from

Steps Involved in Filtering Process of Variables Selection for Final Modelling

Step No.1 Step No.2 Step No.3 Step No.4 Step No.5 Step No. 6

All

Var

iabl

es s

elec

ted

at th

e in

itial

sta

ge

Var

iabl

e ‘C

RO

SS

ING

’ is

use

d at

this

sta

ge to

id

entif

y cr

ossi

ng ID

nu

mbe

r

Var

iabl

e ‘P

OS

XIN

G’ i

s us

ed a

t thi

s st

age

to

iden

tify

posi

tion

of

cros

sing

(R

R O

ver,

RR

U

nder

or

At G

rade

)

Var

iabl

e ‘T

YP

EX

ING

’ is

used

at t

his

stag

e to

id

entif

y ty

pe o

f cr

ossi

ng (

Pub

lic,

Priv

ate

or P

edes

trian

)

Var

iabl

e ‘W

DC

OD

E’ i

s us

ed a

t thi

s st

age

to

iden

tify

prot

ectio

n ty

pe

of c

ross

ings

(S

igns

, S

igna

ls, G

ates

or

Non

e)

Var

iabl

es r

emai

ning

in

filte

ring

proc

ess

for

cons

truc

ting

mod

el

equa

tions

US DOT FRA

Inventory Database

CROSSING - - - - -

POSXING POSXING - - - -

TYPEXING TYPEXING TYPEXING - - -

WDCODE WDCODE WDCODE WDCODE - -

AADT AADT AADT AADT AADT AADT

TOTALTRN TOTALTRN TOTALTRN TOTALTRN TOTALTRN TOTALTRN

MAXTTSPD MAXTTSPD MAXTTSPD MAXTTSPD MAXTTSPD MAXTTSPD

HWYSPEED HWYSPEED HWYSPEED HWYSPEED HWYSPEED HWYSPEED

MAINTRK MAINTRK MAINTRK MAINTRK MAINTRK MAINTRK

TRAFICLN TRAFICLN TRAFICLN TRAFICLN TRAFICLN TRAFICLN

XANGLE XANGLE XANGLE XANGLE XANGLE XANGLE

Given five key characteristics of railway crossings, the first four (CROSSING,

POSXING, TYPEXING and WDCODE) are selected as the basis for identifying

various crossing combinations. For example, the variable of ‘CROSSING’ is used to

identify the ID number of each crossing; ‘POSXING’ indicates whether the crossing

is either At-Grade or Railroad-Under or Railroad-Over; ‘TYPEXING’ shows the

type (whether the crossing is either Public or Private or Pedestrian); and ‘WDCODE’

assists in identifying the type of protection used at crossings. Using these four

variables, the group of railway-highway Public Grade crossings are distinguished

from other groups (Private and Pedestrian). The four variables are used to identify

groups and subsequently they do not form part of prediction and consequences

models since each model is based on this selection. The remaining seven variables

are therefore used at the stage of model development. Table 4.1 shows all steps

involved in the filtering process of identifying appropriate variables prior to

developing a final risk assessment model using statistical methods.

4.1.1.3 Extraction of Public Grade Crossings from Inventory Database

Figure 4.2 shows the extraction process of public grade crossing inventory

information from the USDOT FRA safety inventory database. There are 394,396

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railway-highway crossings (including 249,054 public, 141,081 private and 4,261

pedestrian) in the USA covering a wide spectrum of physical characteristics, warning

devices and usage. Some crossings are equipped only with crossing signs with

reflectors, while others have flashing lights, cantilevers, and gates. These warning

devices are meant to synchronise with adjacent traffic lights to improve flow and to

reduce delays at crossings.

The 249,054 public railway-highway crossings include 209,975 At Grades crossings,

21,362 Railroad-Under crossings and 17,717 Railroad-Over crossings. As outlined

earlier, all 209,975 public grade crossings with the major characteristics are

considered for the purpose of modelling and analysis in this study. Many public

grade crossings are located in remote rural areas, where road and rail traffic volumes

are low. For these crossings, generally no signalised control device is provided. The

trend in recent years, however, has been to upgrade many unsignalised crossings to

include fully automated warning devices with traffic separation barriers. The total

number of crossings identified by a combination of the position of crossing and type

of crossing are shown in Table 4.2. Total of 249,054 public crossings comprise of

209,975 At-Grade, 21,362 RR-Under and 17,717 RR-Over positions. Only public

grade crossings are considered in this study for analysis, which accounted for more

than 53% of all crossings in the USA.

Table 4.2: Number of All Crossings by Type Vs Position (2001-2005)

Type of Crossing Position of Crossing

Grand Total At Grade RR Under RR Over

Pedestrian 2,856 756 649 4,261

Private 137,568 525 2,988 141,081

Publi c 209,975 21,362 17,717 249,054

Grand Total 350,399 22,643 21,354 394,396

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Data Extraction

Information used for data analysis and model

develo pment

Crossing Protection Type 1:

No Signs or No Signals

(11,274 crossings)

Crossing Protection Type 2:

Stop Signs or Cross-bucks

(117,307 crossings)

Crossing Protection Type 3:

Signals, Bells or Warning Devices

(39,397 crossings)

Crossing Protection Type 4:

Gates or

Full Barriers (41,997 crossings)

All Crossings Safety Information - Five Years (2001 – 2005) Period (394,396 crossings available in total)

US DOT FRA Railway Crossings Safety Inventory Database

Private Crossings (141,081 crossings)

Public Crossings(249,054 crossings)

Pedestrian Crossings(4,261 crossings)

Railroad Unde r (21,362 crossings)

At Grade Crossings(209,975 crossings)

Railroad Ove r (17,717 crossings)

Data Analysis

Figure 4.2: Process for Extraction of Public Grade Crossings from Inventory Database

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4.1.2 Database of Railway-Hi ghway Crossing Accidents

Information (Occurrence Database)

A collision is a reportable unexpected event, usually but not exclusively involving an

impact between a train and a highway vehicle. In this study, the terms “collisions”,

“accidents” or “crashes” are treated interchangeably, recognising that one

jurisdiction will favour one term over the others. Collision data is collected from the

USDOT FRA occurrence (or accident) database, which includes necessary detailed

information on each collision over the 394,396 railway-highway crossings for the

period between 2001 and 2005 (see Figure 4.2).

4.1.2.1 Attributes and Variables in Occurrence Database

Similar to an inventory database, an occurrence (or accident) database comprises

many variables. There are 99 variables, related to accidents at crossings, where

details of the database are shown in Table A1-2 in Appendix 1. However, it was

noted from database records that most of the variables are found to have either:

• Incomplete or missing information; or

• Information not relevant for the analysis; or

• Information forming part of another variable; or

• Duplicating another variable already selected for the analysis.

Figure 4.3 depicts the distribution of these groups of variables among the variables

that were selected for initial modelling for prediction of accidents and consequences.

The highest percentage of variables are found in the group in which the variables

have no obvious relevancy in making models (55.6%) followed by the group in

which variables partially reflect others selected for model predictions (16.2%); the

group of variables with incomplete or missing information (14.1%); and then the

group of variable duplicating another variable already selected for the analysis

(8.1%). After eliminating all of the variables described above, there are only

6 variables (6.1% of total variables) that appear to be suitable for initial selection.

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Variables selected for models

6.1%

Duplication of another variable

selected for models 8.1%

Only few records available in the

database14.1%

Part of another variable selected

for models16.2%

Not relevent for model prediction

55.6%

Distribution of selected and non-selected variables from occurrence database

Figure 4.3: Distribution of Different Categories of Variables in the Occurrence Database

4.1.2.2 Selection of Appropriate Variables for Developing Models

For the purpose of models development, all relevant variables are selected initially

by non-statistical method, followed by statistical methods. According to non-

statistical method the variables, which have extremely higher data quality issues, are

eliminated in the first instance. As explained in the previous section, after the

elimination, among the 99 variables identified in the occurrence database a total of

six (6) variables were initially selected for the models development by this method.

These six variables with some descriptive information are briefly discussed below.

Number of People Killed in Acc ident (TOTKLD): This variable provides

information on the number of fatalities resulting from each accident. It varies from

the range of 0 to 7 fatalities in the database.

Number of People Injur ed in Acc ident (TOTINJ): This variable provides

information on the number of injuries resulting from each accident. It varies from the

range of 0 to 35 injuries in the database.

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Highw ay Vehic le Property Da mage in Acc ident (VEHDMG): This variable

provides information on the extent of highway vehicle property damage ($) resulting

from each accident. It varies from the range of 0 to 250,000 dollars in the database.

Tota l Occupants in Vehic le Involved in Acc ident (TO TOCC): This variable

provides information on the total occupancy of each vehicle involved in an accident.

It varies from the range of 0 to 31 persons in the database.

Crossing Locat ion Ident ificat ion (GXID): As described in the previous section on

inventory database, each crossing recorded in the accident database has a

Crossing ID number which indicates its location by street, city, county and state. Use

of common crossing reference numbers (Crossing ID) enables linking both the

inventory and accident databases.

Year of Acc ident (YEAR): This variable refers to the year of railway–highway

accident occurred. Given accidents at crossings during the period of 2001-2005 are

considered in this study, it is noted that there is a total of 14,900 accidents reported

over this period.

Over the period between 2001 and 2005, two (i.e. GXID and YEAR) of the six

variables selected by non-statistical method are initially used to identify the group of

crossings experiencing accidents in the five-year period. For example, the variable of

‘GXID’ is used to identify the ID number of each crossing; and ‘YEAR’ assists in

identifying the year the accident occurred. Once the grouping of crossings is

identified, these two variables are no longer applied to generate models further. The

remaining four variables are therefore used at the stage of model development.

Table 4.3 shows all steps involved in the filtering process of identifying appropriate

variables prior to the development of mathematical models using statistical methods.

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Table 4.3: Filtering Process in Selecting Appropriate Variables from Accident Database

Name of database

where variables

are obtained

from

Steps Involved in Filtering Process of Variables Selection for Final Mo delling

Step No.1 Step No.2 Step No.3 Step No.4

Var

iabl

es

sele

cted

initi

ally

fo

r m

odel

ing

purp

ose

Var

iabl

e ‘G

XID

’ is

use

d at

this

st

age

to id

entif

y cr

ossi

ng ID

nu

mbe

r

Var

iabl

e ‘Y

EA

R’

is u

sed

at th

is

stag

e to

sel

ect

five

year

per

iod

of a

ccid

ents

(2

001

- 20

05)

Var

iabl

es

rem

aini

ng in

fil

terin

g pr

oces

s fo

r co

nstr

uctin

g fin

al m

athe

mat

ic

mod

el

US DOT FRA

Occurrence Database

GXID - - -

YEAR YEAR - -

TOTKLD TOTKLD TOTKLD TOTKLD

TOTINJ TOTINJ TOTINJ TOTINJ

VEHDMG VEHDMG VEHDMG VEHDMG

TOTOCC TOTOCC TOTOCC TOTOCC

4.1.2.3 Selection of Appropriate Records from Occurrence Database

Figure 4.4 shows the extraction process of public grade crossing accidents and

consequences of accidents data from the USDOT FRA collision database for the

preparation of developing models. The data extraction process is based on three

levels of crossing characteristics;

• Type of crossing (Private / Public / Pedestrian);

• Position of crossing (Railroad-Under / Railroad-Over / At Grade); and

• Protection type at crossing (No signs / Stop signs / Signals / Gates).

Based on the above selection criteria, the total number of records under each

protection area is identified and is shown in Figure 4.4.

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153

Data used for model development and

validation

All Crossings Collisions Data - Five Years (2001 – 2005) Period (14,900 records available in total)

US DOT FRA Railway Crossings Collision Database

Private Crossings (1,817 records)

Public Crossings(13,056 records)

Pedestrian Crossings (27 records)

Crossing Protection

Type 1:

No Signs or No Signals (91 records)

Crossing Protection

Type 2:

Stop Signs or Cross-bucks

(4,743 records)

Crossing Protection

Type 3:

Signals, Bells or Warning Devices (2,723 records)

Crossing Protection

Type 4:

Gates or Full Barriers

(5,442 records)

Railroad Under (29 records)

At Grade Crossings(12,999 records)

Railroad Over (28 records)

Data Extraction

Data Analysis

Figure 4.4: Process for Extraction of Crossings Accidents Information

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154

4.1.3 Consolidated Database by Combining Inventory and

Occurrence Databases

As stated in the previous chapter, model development is based on the accidents and

their consequences at public grade crossings. The USDOT FRA inventory database

contains information on 209,975 public grade crossings in the USA. A total of

12,999 collisions (at 10,510 crossings) were reported over the period 2001-2005 in

the USDOT FRA accident database. Accident frequencies at a crossing range from 1

to 15 across 10,510 accident locations. Since data/information on collisions and

grade crossing characteristics are obtained from two separate databases, a common

crossing reference number (Crossing ID) is used to link those databases. A new

consolidated database is developed by linking two individual databases using the

MS Access database management system. Records of the inventory and the

occurrence databases are subsequently combined in the consolidated database to

calibrate and validate the collision frequency and collision consequences prediction

models. The data and information from the consolidated database in MS Access are

finally transferred into SPSS (V15) statistical software system for the purpose of

statistical testing mathematical models.

Two individual dependent variables are newly created for the prediction of accident

frequencies and consequences at crossings separately. The first variable is the

expected number of accidents for accident frequency models. It is predicted by using

a newly created variable ‘ACCCNT’ (total number of accidents recorded per

crossing over the five-year period). The second variable is the expected

consequences per collision for consequence models. The consequences are described

with reference to a broader term of ‘Equivalent Fatality’ (denoted by another newly

created variable ‘EQVFATAL’) by combining the variables TOTKLD (number of

total fatalities), TOTINJ (number of total injuries) and VEHDMG (highway vehicle

and property damage in dollars).

According to the non-statistical method described earlier, a total of eleven variables

(seven from inventory database and four from occurrence database) are initially

selected in developing models. Within the eleven, three variables (TOTKLD,

TOTINJ and VEHDMG) have been used to explain the dependent variable

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(Equivalent Fatality) in order to develop consequences models. The remaining

variables (AADT, TOTALTRN, MAXTTSPD, HWYSPEED, MAINTRK,

TRAFICLN, XANGLE and TOTOCC) are used as independent variables in

developing both accident frequencies and consequences models. A tabular form of

descriptive statistics and graphical presentation on the distribution of independent

and dependant variables for each protection type of level crossings are shown in

Appendix-2.

Further, accident frequency and consequences prediction models are generated using

GLM techniques with SPSS (V15) statistical software package. In GLM modelling,

the variables of AADT, TOTALTRN, MAINTRK, TRAFICLN, and TOTOCC are

used as covariates. Apart from covariates, the variables of MAXTTSPD,

HWYSPEED and XANGLE are used as factors. Developing Best-Fit models is a

forward procedure by which the independent variables are added to a model one by

one. The decision on whether a variable should be retained in the model is based on

statistical measures that can be used to assess the goodness of fit of GLM models.

The two statistical measures used in this study are scaled deviance and Pearson2χ .

The development of such a model is described in the next chapter.

4.2 Preliminary Data Analysis on Rail Crossings Accidents

In order to identify the public grade crossings with high potential risk on the rail

network (so called black-spots), the main purpose of this research, data analysis is

focused on assessing and prioritising the safety risk at public grade crossings by

means of analysing crossing accidents data and consequences. Preliminary data

analysis is therefore initially conducted on accidents data to justify the reasons why

and how the public grade crossings is chosen among other crossing types such as

private and pedestrian, with the combination of crossing position types such as

Railroad-Under and Railroad-Over. It also aims to identify the reason for grouping

public grade crossings by four types of maximum protection by analysis.

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156

4.2.1 Accidents at All Ra ilway-Highway Crossings

Based on the data extracted, each year approximately 363 people lose their lives and

approximately 1034 people are injured as a direct result of all crossing collisions

occurring in the USA at the annual accident average of 2980 approximately

(Table 4.4).

Table 4.4: All Level Crossing Accidents and Casualties (2001 – 2005)

Year Number of

Accidents

Number of

Fatalities

Number of

Injuries

2001 3,135 413 1,136

2002 2,986 353 977

2003 2,870 328 1,007

2004 2,958 368 1,058

2005 2,951 352 991

Grand Total 14,900 1,814 5,169

Average 2,980 363 1,034

It can be noted from Table 4.4 that the total number of crossing collisions has been

decreasing from 2001 to 2005. This trend is illustrated in Figure 4.5. However, over

this period the average number of injuries and fatalities at crossing remained

relatively constant. Although there has been a reduction in the number of collisions

at the rate of nearly 40 per year, the number is still high and needs to be further

reduced for increasing rail safety. As the total trains travelled distance varies from

year to year, the annual accidents data need to be normalised for analysis. In order to

normalise the accidents data over the period, an index (so called Annual Accident

Rate) is defined and described below. This type of index is generally used for

normalisation of accidents in rail industries.

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157

All Crossings Accidents and Casualties

413353 328 368 352

1136

977 10071058

991

0

200

400

600

800

1000

1200

2001 2002 2003 2004 2005

Year

Num

ber

of C

asua

lties

0

500

1000

1500

2000

2500

3000

3500

Num

ber

of A

ccid

ents

Number of Fatalities Number of Injuries Number of Accidents

Figure 4.5: All Level Crossing Accidents and Casualties (2001 – 2005)

4.2.1.1 Annual Accident Rates for All Rail Crossings Relations to Travel

Annual Accident Rate is used to normalise the accidents data in railways. It is

defined as the number of accidents times a million per the total trains travelled

distance (in miles) in the same year. For example, the accident rate for all level

crossing types for the year of 2001 is calculated as:

distance travelled trainsTotal

1,000,000year x per accidents ofNumber RateAccident =

0711,430,00

1000000 x 3,135=

4.41=

Similarly, the accident rates are calculated for other years and tabulated in Table 4.5

and depicted in Figure 4.6. It is noted that the annual accident rate has also been

slightly decreasing during the period between 2001 and 2005.

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158

Table 4.5: Number of All Level Crossing Accidents and Accident Rates (2001 – 2005)

Year Number of

Accidents

Total Train

Miles

Accident

Rate

2001 3,135 711,430,000 4.41

2002 2,986 729,150,000 4.10

2003 2,870 744,250,000 3.86

2004 2,958 770,680,000 3.84

2005 2,951 789,610,000 3.74

Grand Total 14,900 3,745,120,000 3.98

Number of All Crossing Accidents and Rates

31352986 2870 2958 2951

3.743.843.864.104.41

0

500

1000

1500

2000

2500

3000

3500

2001 2002 2003 2004 2005

Year

Num

ber

of A

ccid

ents

0.00

1.00

2.00

3.00

4.00

5.00

Acc

iden

t Rat

eTotal Accidents Accident Rate

Figure 4.6: Number of All Level Crossing Accidents and Accident Rates (2001 – 2005)

The number of accidents for the five-year period by crossing type is shown in

Figure 4.7. In this period, the highest number of collisions (about 88%) occurred at

public crossings followed by private crossings (12 %), with a very negligible number

of accidents at pedestrian crossings.

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159

Number of Accidents by Crossing Type (Year 2001-2005)

27632631 2527 2575 2560

5 5 6 5 6

385378337350367

0

500

1000

1500

2000

2500

3000

2001 2002 2003 2004 2005

Year

Num

ber

of A

ccid

ents

Public Crossing Private Crossing Pedestrian Crossing

Figure 4.7: Number of Level Crossing Accidents by Crossing Type (2001 – 2005)

4.2.1.2 Annual Accident Frequency Rates for Rail Crossings

Annual Accident Frequency Rate is another form of normalising the accidents data in

rail industries. Annual accident frequency rate for a particular type of crossing is

defined as the number of accidents per year times 1000 per same type of crossings.

For example, the annual accident frequency rate for all public crossings is calculated

as:

crossings ofNumber

1,000year x per accidents ofNumber RateFrequencyAccident =

249,054

1,000 x 5) / (13,056=

10.5=

Similarly, the annual accident frequency rates are calculated for other types of

crossings. The frequency rates are tabulated in Table 4.6 and are depicted in

Figure 4.8. The figure shows that the number of annual accidents and the annual

accidents frequency rate for public railway-highway crossings are exceptionally high

values (2,611.2 and 10.5 respectively) in comparison with other types of crossings.

Given the significance of public railway-highway crossings with large number of

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160

accidents, this research study is focusing initially on analysing accidents aspects of

public railway-highway crossings.

 

Annual Accident Frequency Rate per Crossing Type

5.4

363.4

2,611.2

10.5

1.3

2.6

0

1,000

2,000

3,000

Public Private Pedestrian

Type of Crossing

Num

ber of

Acc

iden

ts p

er Y

ear

-

5.0

10.0

15.0

Ann

ual A

ccid

ent F

requ

ency

Rat

e

Number of Accidents per Year Annual Accident Frequency Rate

Figure 4.8: Annual Accident Frequency Rate per Crossing Type

Table 4.6: Accident Frequency Rates by Type of Crossings

Type of Crossing Number of Crossings

Number of Accidents in 5

Year Period

Percentage of Accidents

Annual Accident Frequency Rate

Public 249,054 13,056 87.6 10.5

Private 141,081 1,817 12.2 2.6

Pedestrian 4,261 27 0.2 1.3

Grand Total 394,396 14,900 100.0 7.6

4.2.1.3 Reasons for Research Focus on Public Grade Crossings

Railway-highway crossing collisions are a source of concern for highway regulators,

railway authorities and the public. There were 249,054 public railway-highway

crossings identified in the inventory database, in which a total of 13,056 collisions

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161

were reported across those crossings over the five-year period (2001-2005) in the

USA. This total comprises 12,999, 29 and 28 collisions at-grades, Railroad-Under

and Railroad-Over crossings respectively.

Table 4.7 shows detailed information such as the number of crossings, the number of

accidents and annual accident frequency rates for each type of crossing by their

positions. This information is also individually depicted in Figures 4.9, 4.10 and 4.11

respectively. It is noted that the number of crossings, number of accidents and annual

accident frequency rates for public grade crossings seem to be exceptionally high

compared with the combination of other crossing types.

Table 4.7: Accident Frequency Rates by Type by Position of Crossings

Type of Crossing

Position of Crossing

Number of Crossings

Number of Accidents in 5 Years

Annual Accident Frequency Rate

Public

At-Grade 209,975 12,999 12.4

RR-Under 21,362 29 0.3

RR-Over 17,717 28 0.3

Private

At-Grade 137,568 1,814 2.6

RR-Under 525 2 0.8

RR-Over 2,988 1 0.1

Pedestrian

At-Grade 2,856 23 1.6

RR-Under 756 3 0.8

RR-Over 649 1 0.3

Grand Total 394,396 14,900 7.6

Number of Crossings Vs Crossing Type

137,568

209,975

7562,856

525

21,362

17,7172,988649

0

50,000

100,000

150,000

200,000

250,000

Pedestrian Private Public

Type of Crossing

Num

ber of

Cro

ssin

gs

At Grade RR Under RR Over

Figure 4.9: Number of Crossings within Each Type of Crossing (2001 – 2005)

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162

Number of Accidents Vs Crossing Type

1,814

12,999

3 2 2923

28110

5000

10000

15000

Pedestrian Private Public

Type of Crossing

Num

ber o

f Acc

iden

ts

At Grade RR Under RR Over

Figure 4.10: Number of Accidents within Each Type of Crossing (2001 – 2005)

Accident Frequency Rate Vs Crossing Type

12.4

0.3 0.1 0.3

2.61.60.8 0.8 0.3

0

5

10

15

Pedestrian Private Public

Type of Crossing

Acc

iden

t Fre

quen

cy R

ate

At Grade RR Under RR Over

Figure 4.11: Accident Frequency Rates within Each Type of Crossing (2001 – 2005)

As indicated earlier, the annual accident frequency rate for public railway-highway

grade crossings shows exceptionally high value (12.4) in comparison with other

crossing types (Figure 4.11). Based on the high value of annual accident frequency

rate, the process of assessing safety risk at public grade crossings should be initiated

and safety intervention programs are urgently required for these types of crossings to

improve safety. Therefore, this research study mainly focuses on assessing risks at

public grade crossings through accidents and consequences. Given this focus,

collisions that take place at private or pedestrian crossings are not considered as part

of this study. In addition, this study aims to provide suggestions for improving safety

in particular at crossings with high potential risk on the rail network (so called black-

spots).

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4.2.2 Accidents and Consequences at Public Grade Crossings

As stated earlier, 12,999 collisions occurred at 10,510 crossings across a total

network of 209,975 public grade crossings in the USA over the period 2001-2005.

These records of 12,999 collisions are selected in the mathematical models

development. Over the selected five-year period records shows 1,627 fatalities and

4,545 injuries and these accidents cost more than 65 million dollars worth of

highway property and vehicle damage. The statistical information of collisions and

consequences by the year are summarised in Table 4.8 and depicted in Figure 4.12.

Table 4.8: Public Grade Crossing Accident Casualties (2001 – 2005)

Year Number of

Accidents

Number of

Fatalities

Number of

Injuries

Property Vehicle

Damage ($)

2001 2,745 372 1,020 14,425,519

2002 2,617 311 847 14,164,202

2003 2,517 293 896 12,672,189

2004 2,568 333 926 11,780,402

2005 2,552 318 856 12,413,822

Grand Total 12,999 1,627 4,545 65,456,134

Public Crossings Accidents and Casualties

372311 293 333 318

1020847 896

926856

0

200

400

600

800

1000

1200

2001 2002 2003 2004 2005

Year

Num

ber of

Cas

ualti

es

0

500

1000

1500

2000

2500

3000

3500

Num

ber of

Acc

iden

ts

Number of Fatalities Number of Injuries Number of Accidents

Figure 4.12: Public Grade Crossing Accidents and Casualties (2001 – 2005)

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164

4.2.2.1 Reasons for Grouping Public Grade Crossings by Protection Types for

Model Development

Accident frequency and consequence prediction models were initially developed for

the protection of all types of public grade crossings. However, the results of these

models did not statistically show a reasonable goodness of fit for validation. It was

therefore considered that all types of public grade crossings should not be included in

the same model. For this reason, in order to develop individual accident frequency

and consequence prediction models, all public grade crossings are categorised in to

four groups as described below, based on the type of protection at the crossing,

ranging from minimum protection (Type 1) to maximum protection (Type 4).

• Crossing Protection Type 1: No Signs or No signals

• Crossing Protection Type 2: Stop Signs or Cross-bucks

• Crossing Protection Type 3: Signals, Bells or Warning Devices

• Crossing Protection Type 4: Gates or Full Barrier

4.2.2.2 Inventory Data on Public Grade Crossings by Protection Type

Details of public grade crossings by each type of protection as reported in the

USDOT FRA inventory database are provided in Table 4.9. Accident and

consequences data associated with these crossings have been used in the

development of individual frequency and consequence prediction models. Seven

major variables (Number of main tracks, Track crossing angles, Maximum train

speed, Posted vehicle speed, Daily train movement, Annual average daily traffic,

Number of traffic lanes) are cited in this database. Graphical presentation of each

attribute over a range of crossings for each type of protection is presented in

Appendix 2 (Figure A2-1 to Figure A2-28) for qualitative analysis of those variables,

such as trends, patterns, etc.

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Table 4.9: Public Grade Crossings Data by Protection Type (2001 – 2005)

Type of Protection Number of Crossings

Type 1: No Signs or No signals 11,274

Type 2: Stop Signs or Cross-bucks 117,307

Type 3: Signals, Bells or Warning Devices 39,397

Type 4: Gates or Full Barrier 41,997

Grand Total 209,975

4.2.2.3 Statistics of Accident Frequency and Consequence for Public Grade

Crossings by Protection Type (2001 – 2005)

Tables 4.10 and 4.11 provide a summary of the statistics for the accidents and

casualties respectively at the public grade crossings by each type of protection. For

the period 2001-2005, the maximum number of the following variables per crossing

is observed as:

• 15 Collisions;

• 5 Fatalities;

• 35 Injuries; and

• 0.5 million dollars worth of highway property and vehicle damage.

Table 4.10: Accidents Data of Public Grade Crossings by Protection Type (2001-2005)

Type of Protection

Number

of

Crossings

Number of

Accidental

Crossings

Number of

Accidents

Type 1: No Signs or No signals 11,274 84 91

Type 2: Stop Signs or Cross-bucks 117,307 3,998 4,743

Type 3: Signals, Bells or Warning Devices 39,397 2,130 2,723

Type 4: Gates or Full Barrier 41,997 4,298 5,442

Grand Total 209,975 10,510 12,999

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Table 4.11: Consequence Data of Public Grade Crossings by Protection Type (2001-2005)

Type of Protection Number of

Fatalities

Number of

Injuries

Vehicle property

damage ($)

Type 1: No Signs or No signals 1 20 369,250

Type 2: Stop Signs or Cross-bucks 503 1,846 26,008,425

Type 3: Signals, Bells or Warning Devices 248 887 12,061,768

Type 4: Gates or Full Barrier 875 1,792 27,016,691

Grand Total 1,627 4,54 5 65,456,134

4.2.2.4 Statistics of Variables Used in Models by Protection Types

A significant amount of variation in the data is observed for AADT - number of

trains, daily train speed, road speed, number of tracks, and number of traffic lanes.

There is also a significant variation in exposure among various protection types of

crossings in the data set. Tables A3-1, A3-3, A3-5 and A3-7 in Appendix 3 show that

descriptive statistics of variables, which demonstrate significant variation in values,

have been used in the development of collision prediction models by each protection

type. Meanwhile, statistical descriptions of variables, which have been used in the

development of consequences prediction models by each protection type, are shown

in Tables (A3-2, A3-4, A3-6 and A3-8) in Appendix 3.

4.3 Summary

It is noted that the proposed approach for risk assessment models needs considerable

amount of data on accidents and consequences as well as details of railway crossing

characteristics/factors. Thus, various data sources were considered, including

Australian and US data across large rail networks. Subsequently, a relevant data

with required information over a period of five years (2001-2005) was selected,

using a combination of two major databases (Safety Inventory database and

Occurrence database) provided by the United States Department of Transportation

Federal Railroad Administration (USDOT FRA). The inventory database is

characterised by several attributes based on the static data and information on

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geometric characteristics of highways and railways, traffic control and volume for

each of the crossings in the USA. Due to data quality issues, only eleven major

attributes from the inventory database have been selected and collated for initial

analysis in this study. The occurrence database contains the information such as

collision (date, time, location etc.) and consequence (fatalities, injuries and property

damage, etc.). Four attributes from the occurrence database have been selected for

the analysis. As the preliminary analysis showed that the annual accident frequency

rate for public grade crossings was exceptionally higher than other types of

crossings, the research is focused on assessing and prioritising risks at public grade

crossings through the combination of accidents and consequences. The collisions at

private or pedestrian crossings are omitted for the analysis in this study.

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Chapter 5

Development and Validation of Grade Crossing Accidents and Consequences Prediction Models

5.0 Introduction

Prediction of accidents and consequences at railway grade crossings is an integral

part of overall risk assessment models, and is carried out using the development and

validation of individual models based on data and information collected and

reported earlier in the previous chapter. In this case, models are developed and

validated using a set of data collected from two different databases of inventory and

accident data across the large railway infrastructure of the USA. In the model

development stage, all possible protection measures at grade crossings of USA rail

infrastructure are categorised into four protection groups, as described earlier.

These protection groups, along with possible explanatory factors and their variables

outlined in Chapter 4, are considered to be major pillars of risk assessment models

since different protection groups could influence differently the occurrence of

accidents and consequences at grade crossings.

This chapter describes the process of model development using those explanatory

factors and the variables, leading to identification of black-spots in railway-highway

grade crossings in the USA. The process is organised into two stages. In the first

stage, a set of accident frequency models is developed and validated using USA

railway crossings accidents data. This would enable identification of the most

appropriate accident frequency model. At the next stage, the same procedure is

repeated to identify the most appropriate accidental consequences models. All

distinctive accident frequency and accidental consequences prediction models are

individually developed for each group of all four protection types.

The chapter is structured as follows. Firstly, a review of previously considered safety

risk assessment models is presented, followed by an overview of current accident

prediction models, in particular Poisson and Negative binomial models. Next, an

overview of existing consequence prediction models is presented. Accident and

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consequences prediction models are then presented with validation procedures and

results. Finally, the chapter concludes on model development and validation.

5.1 Overview of Current S afety Risk Assessment Models

There has been increased emphasis on railway safety management in recent years

due to implementation of new legislative procedures and publications of safety

management system standards in various countries such as the USA, Canada, UK,

Korea, New Zealand and Australia. These documents show that the countries agree

that the risk assessment process is a key to SMS. The documents also indicate that a

safety risk assessment is made up of two main parts:

(a) Probability (likelihood) of occurrence of an incident; and

(b) Severity of the incident’s consequences.

In general, an incident is defined as an unintentional and undesirable event that may

or may not result in an injury. An incident that results in an injury, fatality or

property damage is defined as an accident. This definition clearly indicates that the

occurrence of an incident or accident at railway grade crossings is a random event

caused by several factors such as window of accident opportunity, chance and luck,

which are frequently mentioned in the incident causation literatures

(McKinnon 2000; Reason 1990; Sanders & Shaw 1988; Ramsey 1985). However,

randomness does not refer to events without causes or unaffected by human

mistakes, and infrastructure and system failures, but instead to the presence of

variations. In the statistical sense, variation means that two situations with similar

characteristics will not guarantee the same outcome (Montgomery & Runger 1999).

This type of random process may be statistically modelled to characterise and

analyse systematically the risk posed by railway incidents or accidents. In this study

the statistical approach will analyse the grade crossing accidents based on a stable

and sound foundation provided by mathematical boundaries and reasoning, thus

improving the effectiveness of railway safety management.

Statistical models have frequently been used in highway safety studies. They can be

utilised for various purposes, including establishing relationships between variables,

screening covariates and predicting values. Generalised Linear Model (GLM) has

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been one of the most common types of model favoured by transportation safety

analysts (Xie, Lord & Zhang 2006). Several road traffic safety researchers generated

models to predict road accidents and the severity of consequences (Hutchinson &

Mayne 1977; Ivan, Wang & Bernardo 2000; Joshua & Garber 1990; Kuan, Peck &

Janke 1991; Kulmala 1995; Long 2003; Lord, Washington & Ivan 2004; Lyon et al.

2003; Miaou 1993; Nassar, Saccomanno & Shortreed 1994; Oh et al. 2003; Persaud

& Dzbik 1993; Philipson, Fleischer & Rashti 1981; Poch & Mannering 1996).

However, only a few railway safety researchers carried out formal studies to model

railway-highway grade crossing accidents statistically (Austin & Carson 2002; Berg,

Knoblauch & Hucke 1982; Laffey 1999; Oh et al. 2006; Saccomanno et al. 2001).

Traffic safety and reliability engineering researchers have used numerous probability

distributions to model the occurrence of incidents in their respective areas, and one

of the most commonly used probability distributions is the Poisson distribution

(Modarres, Kaminskiy & Krivtsov 1999; Fridstrom et al. 1995; Bendell, Disney &

McCollin 1999). However, because of differences in the scale, environment, and

nature of the processes, it would be prudent to verify that the Poisson distributions

are suitable for modelling the nature of railway grade crossings accidents.

Consequently this study presents a suitable statistical interpretation of accident

occurrences. Accident data from all railway grade crossings in the USA from the

years of 2001 to 2005 have been used in the statistical tests, goodness-of-fit of the

distributions, modelling and the randomness of the accidents. The model is initially

extended to incorporate the concepts of a modified Poisson version in order to

include accident frequency in the past history.

5.2 Common Models of Accident Frequency Prediction

In this study, common types of accident prediction models were initially identified

from various publications written by several researchers. The common types of

accident prediction models include Poisson, Negative Binomial (NB) and Empirical

Bayesian (EB) models. These models are individually generated with accident data

in USDOT FRA occurrence database and tested for their goodness-of-fit. These

models are individually formed with four distinctive expressions, depending on types

of protection (i.e. 1.No Signs or No signals / 2.Stop Signs or Cross-bucks / 3.Signals,

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Bells or Warning Devices / 4.Gates or Full Barrier) as shown in the Section 4.1.1.2

of previous chapter. These types of accident prediction models are explained below

in detail.

5.2.1 Poisson Models

The Poisson distribution is an appropriate model for count data. Examples of such

data are mortality of infants in a city, the number of misprints in a book, the number

of bacteria on a plate, and the number of activations of a Geiger counter. The Poisson

distribution was derived by the French mathematician Poisson in 1837, and the first

application was the description of the number of deaths by horse kicking in the

Prussian army. The Poisson distribution is a mathematical rule that assigns

probabilities to the number occurrences. The only thing we have to know to specify

the Poisson distribution is the mean number of occurrences. Generally, for small

values of mean, the distribution is not symmetric but skewed. This is a general

property when the mean is small. The distribution becomes more symmetric when

the mean is larger. A property of this distribution is that the variance is equal to the

mean. The Poisson distribution resembles the binomial distribution when the

probability of an event is very small.

5.2.1.1 Poisson Distribution

Simple Poisson models are based on the assumption that the count observation (Y) in

any time interval ‘t’ was a random variable with Poisson probability mass function

(Po). The commonly applied statistical model for a count distribution is the Poisson

model in which it is assumed that Y follows a Poisson density:

), |(y Po = y!/ )( = y) = p(Y ty

tte λλλ− (5.1)

where:

y is the number of accidents and non-negative integer values (i.e. 0,1,2,……….);

p is the Poisson probability mass function in a given time interval ‘t’; and

λ is the accident occurrence rate (number of accidents per 5 years)

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Demonstrat ion of Simple Poisson Model Predic t ing Acc idents a t Grade

Crossings by Protect ion Types

Using the Poisson density equation, the probabilities of accidents for the counts

(0,1,2....) were initially calculated. The number of crossings for each count was then

predicted for each types of protection and the result is summarised in Table 5.1. It is

noted there are excessive zeros in the accident history. This means there was a large

number of crossings which did not experienced accidents in the five-year period of

interest. By comparing the number of crossings predicted by the Poisson model and

the observed number in the history, it was noted that there was no close match

between these two numbers. The differences of these two numbers in each type of

protection at crossings are also shown in the graphical demonstration in Figures 5.1,

5.2, 5.3 and 5.4. It can also be noted that for all types of protection, the mean values

of number of collisions show far less than the variances.

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Table 5.1: Comparison of Accidental Crossings Predicted by Poisson Model to History

Group of Crossings

Protection

Type 1

Protection

Type 2

Protection

Type 3

Protection

Type 4

Total Number of Collisions 91 4743 2723 5442

Total Number of Grade Crossings 11274 117306 39397 41997

Mean 0.0081 0.0404 0.0691 0.1296

Variance 0.01 0.0572 0.1136 0.1957

Exponential [ - Mean] 0.992 0.9604 0.9332 0.8785

Number of

Crossings for

Count (in

History):

0 11190 113308 37267 37699

1 80 3414 1731 3513

2 2 480 288 558

3 1 74 72 155

4 1 22 19 41

5 & over 0 8 20 31

Probability of

Collision

(Poisson

Model) for

Count:

0 0.992 0.9604 0.9332 0.8785

1 0.008 0.0388 0.0645 0.1138

2 0 0.0008 0.0022 0.0074

3 0 0 0.0001 0.0003

4 0 0 0 0

5 & over 0 0 0 0

Prediction

Number of

Crossings

(Poisson

Model) for

Count:

0 11183 112658 36766 36893

1 90 4555 2541 4781

2 0 92 88 310

3 0 1 2 13

4 0 0 0 0

5 & over 0 0 0 0

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(a) Crossing Protect ion Type 1 (No Signs or No signals)

Number of Crossings Predicted by Poisson Model - Protection Type 1

0

3000

6000

9000

12000

Number of Accidents

Num

ber

of C

ross

ings

Actual Number in USDOT Database 11190 80 2 1 1 0

Predict ion by Poisson M odel 11183 90 0 0 0 0

0 1 2 3 4 5 & over

Figure 5.1: Number of Crossings Predicted by Poisson Model for Protection Type 1

(b) Crossing Protect ion Type 2 (S top Signs or Cross-bucks)

 

Number of Crossings Predicted by Poisson Model - Protection Type 2

0

30000

60000

90000

120000

Number of Accidents

Num

ber

of C

ross

ings

Actual Number in USDOT Database 113308 3414 480 74 22 8

Predict ion by Poisson M odel 112658 4555 92 1 0 0

0 1 2 3 4 5 & over

Figure 5.2: Number of Crossings Predicted by Poisson Model for Protection Type 2

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175

(c) Crossing Protect ion Type 3 (Signals, Bells or Warni ng Devices)

 

Number of Crossings Predicted by Poisson Model - Protection Type 3

0

10000

20000

30000

40000

Number of Accidents

Num

ber

of C

ross

ings

Actual Number in USDOT Database 37267 1731 288 72 19 20

Predict ion by Poisson M odel 36766 2541 88 2 0 0

0 1 2 3 4 5 & over

Figure 5.3: Number of Crossings Predicted by Poisson Model for Protection Type 3

(d) Crossing Protect ion Type 4 (Gates or Full Barrier)

 

Number of Crossings Predicted by Poisson Model - Protection Type 4

0

10000

20000

30000

40000

Number of Accidents

Num

ber

of C

ross

ings

Actual Number in USDOT Database 37699 3513 558 155 41 31

Predict ion by Poisson M odel 36893 4781 310 13 0 0

0 1 2 3 4 5 & over

Figure 5.4: Number of Crossings Predicted by Poisson Model for Protection Type 4

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5.2.1.2 Zero-Inflated Poisson Distribution

The analysis of count data is of primary interest in many areas including engineering,

mathematics, agriculture, sociology, public health, psychology and others. In

particular, a Poisson model ), |(y Po= y) = p(Y tλ is assumed for modelling the

distribution of the count observation (Y). However, it has been observed (even in the

above-mentioned simple Poisson model) in various applications that the dispersion

of the Poisson model underestimates the observed dispersion. This phenomenon is

called ‘over-dispersion’ and occurs because a single Poisson parameter (_

y ) is often

insufficient to describe the population. In many cases it can be suspected that

population heterogeneity, which has not been accounted for, is causing this over-

dispersion. This population heterogeneity is not observed. In other words, the

population consists of several subpopulations, in this case of the Poisson type, but the

subpopulation membership is not observed in the sample. One possibility to cope

with the problem is to assume that the heterogeneity involved in the data can be

adequately described by some density )(λ∏ and is defined on the population of

possible Poisson parameter (λ ). Since this heterogeneity cannot be observed

directly, it is also called latent heterogeneity. It can only be observed in the counts

coming from the marginal or mixture density (Böhning 1995).

)( ) , |(y Po = ), |y ( F λλλλπ dto

∏∫∞ (5.2)

There are two approaches, which can be distinguished. Firstly, the traditional

approach is to follow a fully parametric model for the mixing density )(λ∏ . A very

good example of this nature model is the Gamma distribution for )(λ∏ , for which

the marginal density becomes the negative binomial. The second one is non-

parametric approach, which does not specify any parametric density for )(λ∏ . In

this case, the non-parametric maximum likelihood estimator (NPMLE) is always

giving weights jπ to the latent classes or subpopulations gλ , g = 1,2,..,G (Simar

1976; Böhning 1982; Lindsay 1983; Böhning 1995). This non-parametric model is

the attractive approach, since it is not only easy to interpret, but also requires no

specification of the number of latent classes G. However both approaches are

connected with the Empirical-Bayes methodology (Maritz & Lwin 1989; Zhang

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177

2003), since an estimate of the distribution )(λ∏ can be viewed as an Empirical-

Bayes estimator, which estimates the prior distribution in the Bayes theorem. Thus,

mixture models provide the tool to classify observations via the maximum posterior

probability into the components or classes of the mixture model. In this case, we

analyse a special form of non-parametric heterogeneity density )(λ∏ . A two mass-

distribution gives mass (ip ) to count zero (0) and (1-ip ) to the second class with

mean λ . In other words, we consider a data situation in which a number of extra

zeros occur.

In this study, the number of accidents over the five-year period (2001 – 2005) is

considered as the count, as it is an important indicator and overall measure for the

safety status of a particular grade crossing. Figures from 5.5 to 5.8 show graphical

comparison of distribution on an estimated number of crossings per number of

accidents (which was predicted by a simple Poisson model) against the actual

number of historical accidents for each type of protection. There is a clear spike of

extra zeros in each type of protection, representing the crossings with no accidental

experience. By looking at the prediction for these cases, however, this simple model

does not fit very well. If the Poisson assumption would be true, expected value and

variance should coincide as per the Poisson’s basic properties.

Since the expected value and variance can be estimated by the sample mean (_

y ) and

the sample variance ( )1(/}2)_

(....2)_

1{(2 −−++−− Ny

ryyys ) respectively, it is

natural to compare 2s and _

y leading to the over-dispersion test value (O) given by

(Böhning, Dietz & Schlattmann 1995):

_)

_2(

2

)1(

y

ysNO

−−=

(5.3)

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178

Table 5.2: Over-Dispersion Test Values on Number of Accidents by Crossing Types

Crossing Group Description Variance (2s )

Mean

(_

y )

Number of

Crossings (N) P-Value

O-Test

Value

Protection Type 1 No Signs or No

signals 0.0100 0.0081 11,274 0.000 17.55

Protection Type 2 Stop Signs or Cross-

bucks 0.0569 0.0404 117,306 0.000 98.87

Protection Type 3 Signals, Bells or

Warning Devices 0.1136 0.0691 39,397 0.002 90.40

Protection Type 4 Gates or Full Barrier 0.1957 0.1296 41,997 0.001 73.95

For example on specimen calculation of this test, consider the data for the crossings

group with protection type 1. The equation 5.3 calculates the value of over-

dispersion test as 17.55 with 2s = 0.0100, _

y = 0.0081, N = 11,274 and P-value

<0.001. The O-Test values for the other groups are also calculated and shown in

Table 5.2. In general, the O-Test values for all crossing groups are considerably

higher than zero value, which indicates the data has strong over-dispersion. This

tendency indicates that a simple Poisson model would not adequate to fit the data.

Instead, the data show strong over-dispersion (2s >_

y ), due to the fact that a large

frequency of extra-zeros has occurred in the distribution. A simple way to model this

zero-inflation is to include a proportion (p) of extra-zeros and a proportion (1-

p) λ−e coming from the Poisson distribution (Johnson, Kotz & Kemp 1992;

Lambert 1992). We can write the Zero-inflated Poisson density F (y| λ,p ) as:

{ }0;),()1(

0;)1(= ) |(y F , >−=−−+

yifyPp

yifeppp λ

λλ (5.4)

where:

!/),( yy

eyPo λλλ −= (5.5)

Since it is one of the properties of the Poisson distribution that 0)0,( =yPo for

y > 0, and 1)0,0( =Po , for simplicity, we shall re-write the equation 5.5 as:

),()1()0,()(= ) |(y F , λλ yPopyPopp −+ (5.6)

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Thus, )0,(yPo is the one point distribution putting all its mass at zero. As a sideline,

we note that this property is not shared by many distributions. For example, the

simple Poisson does not have this property, whereas the binomial does. The

representation of Equation 5.6 points out that the ZIP-model is a special mixture

model having two classes, where the first class has a fixed value at zero (0). This

class can be interpreted according to the type of application, and usually rather

simple interpretations exist. In this case, this class consists of grade crossings with no

accidents experienced at all over the five-year period. The second class has a value

of a non-zero positive integer. This class consists of grade crossings with at least one

accident experienced in the same period. For the ZIP-model with zero-inflation we

find that;

(Y)] E - [ (Y) E + (Y) E = (Y)Var λ (5.7)

and;

λ)1( = (Y) E p− (5.8)

Est imat ion of Model Parameters

Moment Estimation

From the equations 5.7 and 5.8, we have the moment equations: E (Y) =Y and

(Y)] E - + [1 (Y) E = 2 λS which are readily solved by:

+ 1 - / = ˆ 2 YYSMOλ (5.9)

and:

MOMO Yp λ / - 1 =ˆ (5.10)

Maximum Likelihood Estimation (MLE)

Let iN be the number of i's in the sample; in particular, 0N is the number of zeros

in the sample. Then the log-likelihood function is given as:

]),()1([ Log + ])1([ Log = ),( L 1

0 λλλ yPopNeppNpm

x

x −−−+ ∑=

(5.11)

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180

and the score vector:

( ) T

YNNN

epp

epN

p

NN

epp

eN ⎭⎬

⎫⎩⎨⎧ +−−⎟⎟⎠

⎞⎜⎜⎝⎛

−+−−⎟⎟⎠

⎞⎜⎜⎝⎛

−−+⎟⎟⎠

⎞⎜⎜⎝⎛

−+−

−−

−−

λλλ

λλ

000

0 )1(

)1(,

)1()1(

1

(5.12)

leading to the score equations:

⎟⎟⎟⎠⎞

⎜⎜⎜⎝⎛

−−−−= λ

λe

eNNp

1

/0

(5.13)

and:

)1(/ pY −=λ (5.14)

which can be written in one equation:

⎟⎟⎠⎞

⎜⎜⎝⎛

−−−= λλ

e

NNY

1

/0

1/

(5.15)

As the right hand side of the equation 5.15 is a function of ‘λ ’, it may be written as:

⎟⎟⎠⎞

⎜⎜⎝⎛

−−−= λλ

e

NNYG

1

/0

1/)(

(5.16)

The solution for the value of λ can be obtained by iteration method in solving the

equation of:

λλ =)(G (5.17)

The first derivative of the function )(λG with respect to λ is:

⎟⎟⎠⎞

⎜⎜⎝⎛

−−=

NN

eYG

d

d

/0

1)(

λλλ

(5.18)

and the second derivative of the function )(λG with respect to λ is:

⎟⎟⎠⎞

⎜⎜⎝⎛

−−−=

NN

eYG

d

d

/0

1)(

2

2 λλλλ

(5.19)

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From the equations 5.18 and 5.19, it can be seen that the values of )(λλ Gd

d> 0 and

)(2

2 λλ Gd

d < 0. It shows that the graph of )(λG versus λ converges for any initial

value 0λ to the MLE MLEλ satisfying the fixed-point equation λλ =)(G . MOλλ ˆ0 =

might be chosen as the initial value for iteration. The convergence of this algorithm

is usually linear and ways of acceleration do exist (Böhning 1993). Figures 5.5, 5.6,

5.7 and 5.8 show a reasonably close match between the number of crossings

predicted by Zero-Inflated Poisson Model and the observed number in the history.

Demonstrat ion of Zero-Infla ted Poi sson Model Predic t ing Acc idents at

Grade Crossings by Protect ion Types

Figures 5.5 to 5.8 show the graphical comparison of distribution on the estimated

number of crossings per number of accidents, which was predicted by Zero-Inflated

Poisson models, against the actual number of historical accidents for each type of

protection. Table 5.3 summarises the observed and prediction values on the number

of accidents, which were obtained using simple and zero-inflated Poisson Models by

each type of protection. By referring to the values of Pearson Chi-squares (2χ ), even

though the Zip model shows a better goodness-of-fit than the Simple Poisson model

as it contains over-dispersion (2χ >

205.0χ ) issue, we still need to search for a best-fit

model to overcome this issue.

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(a) Crossing Protect ion Type 1 (No Signs or No signals)

Number of Crossings Predicted by ZIP Model - Protection Type 1

0

3000

6000

9000

12000

Number of Accidents

Num

ber

of C

ross

ings

Actual Number in USDOT Database 11190 80 2 1 1 0

Predict ion by ZIP M odel 11190 77 6 0 0 0

0 1 2 3 4 5 & over

Figure 5.5: Number of Crossings Predicted by ZIP Model for Protection Type 1

(b) Crossing Protect ion Type 2 (S top Signs or Cross-bucks)

 

Number of Crossings Predicted by ZIP Model - Protection Type 2

0

30000

60000

90000

120000

Number of Accidents

Num

ber

of C

ross

ings

Actual Number in USDOT Database 113308 3414 480 74 22 8

Predict ion by ZIP M odel 113308 3335 587 69 6 0

0 1 2 3 4 5 & over

Figure 5.6: Number of Crossings Predicted by ZIP Model for Protection Type 2

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(c) Crossing Protect ion Type 3 (Signals, Bells or Warni ng Devices)

 

Number of Crossings Predicted by ZIP Model - Protection Type 3

0

10000

20000

30000

40000

Number of Accidents

Num

ber

of C

ross

ings

Actual Number in USDOT Database 37267 1731 288 72 19 20

Predict ion by ZIP M odel 37267 1630 418 72 9 1

0 1 2 3 4 5 & over

Figure 5.7: Number of Crossings Predicted by ZIP Model for Protection Type 3

(d) Crossing Protect ion Type 4 (Gates or Full Barrier)

 

Number of Crossings Predicted by ZIP Model - Protection Type 4

0

10000

20000

30000

40000

Number of Accidents

Num

ber

of C

ross

ings

Actual Number in USDOT Database 37699 3513 558 155 41 31

Predict ion by ZIP M odel 37699 3327 819 134 17 2

0 1 2 3 4 5 & over

Figure 5.8: Number of Crossings Predicted by ZIP Model for Protection Type 4

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Table 5.3: Comparison of Observed and Predicted Values for Accidental Crossings Obtained from Simple and ZIP Poisson Models

Number of

Accidents

Number of Grade Crossings

Crossing Protection Type 1:

No Signs or No signals

Crossing Protection Type 2:

Stop Signs or Cross-bucks

Crossing Protection Type 3:

Signals, Bells or Warning Devices

Crossing Protection Type 4:

Gates or Full Barrier

Actual number

in DOT FRA

Database

Prediction by

Simple Poisson

Model

Prediction by

ZIP Model

Actual number

in DOT FRA

Database

Prediction by

Simple Poisson

Model

Prediction by

ZIP Model

Actual number

in DOT FRA

Database

Prediction by

Simple Poisson

Model

Prediction by

ZIP Model

Actual number

in DOT FRA

Database

Prediction by

Simple Poisson

Model

Prediction by

ZIP Model

0 11190 11183 11190 113308 112658 113308 37267 36766 37267 37699 36893 37699

1 80 90 77 3414 4555 3335 1731 2541 1630 3513 4781 3327

2 2 0 6 480 92 587 288 88 418 558 310 819

3 1 0 0 74 1 69 72 2 72 155 13 134

4 1 0 0 22 0 6 19 0 9 41 0 17

5 0 0 0 4 0 0 10 0 1 14 0 2

6 0 0 0 0 0 0 4 0 0 10 0 0

7 0 0 0 1 0 0 3 0 0 2 0 0

8 0 0 0 1 0 0 1 0 0 5 0 0

9 0 0 0 1 0 0 1 0 0 0 0 0

10 0 0 0 0 0 0 0 0 0 0 0 0

11 0 0 0 0 0 0 0 0 0 0 0 0

12 0 0 0 0 0 0 1 0 0 0 0 0

13 0 0 0 0 0 0 0 0 0 0 0 0

14 0 0 0 0 0 0 0 0 0 0 0 0

15 0 0 0 1 0 0 0 0 0 0 0 0

Grand Total 11274 11274 11274 117306 117306 117306 39397 39397 39397 41997 41997 41997

2χ - 1.12 2.78 - 7254.91 64.40 - 3169.58 138.80 - 2103.38 202.75

205.0χ

7.82

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5.2.1.3 Multiplicative Poisson Regression Distribution

In general, this type of model is used for predicting numbers of uncommon events

such as railway-highway grade crossing accidents. The multiplicative Poisson

regression model is fitted as a log-linear regression (i.e. a log link and a Poisson error

distribution), with an offset equal to the natural logarithm of person-time if person-

time is specified (McCullagh & Nelder 1989; Frome 1983; Agresti & Coull 2002).

With the multiplicative Poisson model, the exponents of coefficients are equal to the

incidence rate ratio (relative risk). These baseline relative risks give values relative to

named covariates for the whole population. The outcome / response variable is

assumed to come from a Poisson distribution. Note that a Poisson distribution is the

distribution of the number of events in a fixed time interval, provided that the events

occur at random, independently in time and at a constant rate. Poisson distributions

are used for modelling events per unit space as well as time, for example the number

of accidents per number of crossings within a state.

In the past, research companies such as Arthur D. Little Limited focused on the

impacts of railway-highway grade crossings (HRGC) to the safety of corridors, and

decomposed the corridor accidents into different accident scenarios and types.

HRGC was one of the scenarios within the studies. Factors contributing to the

accidents were initially identified and used as reference variables in the regression

models, which could be established in a linear or an exponential density function.

Accident occurrence rate λ can be exponential function of reference variable (iZ ). It

may be written in the form of:

∑== +=

ni

i

iiZba

e 1

)(

λ

(5.20)

Where:

iZ is the ith reference variable;

n is the number of reference variables;

a and ib are the regression parameters and could be obtained by maximizing the

likelihood function of equation 5.1. As λ is the estimated mean ( )(ˆ YE ) obtained by

using the values of reference variables, the equation can be re-written as:

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∑== +=

ni

i

iiZba

YE e 1

)(

)(ˆ

(5.21)

5.2.2 Negative Binomial Regression Model

The Negative Binomial (NB) distribution is traditionally derived from a Poisson–

gamma mixture model. As indicated by Hilbe (2007), it may also be thought of as a

member of the single parameter exponential family of distributions. This family of

distributions admits a characterisation known as Generalized Linear Models (GLMs),

which summarises each member of the family. Most importantly, the characterisation

is applicable to the negative binomial. Such interpretation allows statisticians to

apply to the negative binomial model the various goodness-of-fit tests and residual

analyses that have been developed for GLMs. Poisson regression is the standard

method used to model count response data. However, the Poisson distribution

assumes the equality of its mean and variance - a property that is rarely found in real

data. Data that have greater variance than the mean are termed Poisson over-

dispersed, but are more commonly designated as simply over-dispersed. Negative

binomial regression is a standard method used to model over-dispersed Poisson data.

When the NB is used to model over-dispersed Poisson count data, the distribution

can be thought of as an extension to the Poisson model. The original derivation of the

negative binomial regression model stems from this manner of understanding it, and

has continued to characterize the model to the present time.

As mentioned above, the NB has recently been thought of as having an origin other

than a Poisson-gamma mixture. It may be derived as a generalized linear model, but

only if its ancillary or heterogeneity parameter is entered into the distribution as a

constant. The straightforward derivation of the model from the negative binomial

probability distribution function does not, however, equate with the Poisson–gamma

mixture-based version of the negative binomial. Rather, one must convert the

canonical link and inverse canonical link to log form. So doing produces a GLM-

based negative binomial that yields identical parameter estimates to those calculated

by the mixture based model. As a non-canonical linked model, however, the standard

errors will differ slightly from the mixture model, which is typically estimated using

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a full maximum likelihood procedure. The latter uses by default the observed

information matrix to produce standard errors. The standard GLM algorithm uses

Fisher scoring to produce standard errors based on the expected information matrix,

hence the difference in standard errors between the two versions of negative

binomial. The GLM negative binomial algorithm may be amended, however, to

allow production of standard errors based on observed information. When this is

done, the amended GLM-based negative binomial produces identical estimates and

standard errors to that of the mixture-based negative binomial.

Hilbe (2007) called this form of negative binomial the log-negative binomial. It is the

form of the negative binomial found in SPSSs (Version 15) GLZ command

procedure. Regardless of the manner in which the negative binomial is estimated, it

is nevertheless nearly always used to model Poisson over-dispersion. The advantage

of the GLM approach rests in its ability to utilise the specialised GLM fit and

residual statistics that come with the majority of GLM software. This gives the

analyst the means to quantitatively test different modelling strategies with tools built

into the GLM algorithm. This capability is rarely available with models estimated

using full maximum likelihood or full quasi-likelihood methods. Hilbe, J.M. and a

number of other recent authors have employed the direct relationship as the preferred

variance function. The reason for preferring the direct relationship stems from the

use of the negative binomial in modelling over-dispersed Poisson count data.

Considered in this manner, α is directly related to the amount of over-dispersion in

the data. If the data are not over-dispersed, i.e. the data are Poisson, then α = 0.

Increasing values of α indicate increasing amounts of over-dispersion. Values for

data seen in practice typically range from 0 to about 4. In this study, the negative

binomial was estimated based on GLM. As a GLM, the model has associated fit and

residual statistics, which can be of substantial use during the modelling process.

However, in order to obtain a value of α, i.e. to make α known, it must be estimated.

The traditional and most reasonable method of estimating α is by a non-GLM

maximum likelihood algorithm.

Following an examination of estimating methods and overviews of both the Poisson

and negative binomial models, the negative binomial has greater generality. In fact,

the Poisson can be considered as a negative binomial with an ancillary or

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188

heterogeneity parameter value of zero. It seems clear that having an understanding of

the various negative binomial models, basic as well as complex, is essential for

anyone considering serious research dealing with count models. It is important to

realise that the negative binomial has been derived and presented with different

parameterisations. Some authors employ a variance function that clearly reflects a

Poisson-gamma mixture. With the Poisson variance defined as λ and the gamma as

2λ /α, the negative binomial variance is then characterised as λ + 2λ /α. The Poisson-

gamma mixture is now clear. This parameterisation is the same as that originally

derived by Greenwood and Yule (1920). An inverse relationship between λ and α

was also used to define the negative binomial variance in McCullagh and Nelder

(1989), to which some authors refer when continuing this manner of representation.

5.2.3 Empirical Bayesian (EB) Model

The remainder of the analysis was then devoted to a discussion of how to understand

and deal with some degree of enhancements to the traditional models developed.

Extensions to these models are made depending on the type of underlying problem

that is being addressed. Extended models should be able to overcome the issues such

as handling excessive response zeros; handling responses having no possibility of

zero counts; having responses with structurally absent values; and having

longitudinal or clustered data (Hilbe 2007). Models may also have to be devised for

situations when the data can be split into two or more distributional subsets. In this

study the two methods of developing simple Poisson and negative binomial models

was discussed in greater depth as outlined above. The complete derivation of both

methods is given below, together with a discussion about how the algorithms may be

altered to deal with count data that should be modeled using simple Poisson or

standard negative binomial methods. In fact, the basic Poisson regression model was

described in considerable detail, and the manner in which its assumptions may be

violated. In addition, it was found that as Poisson models are slightly over-dispersed,

the negative binomial models were then developed to overcome this problem.

Typically, extensions to the Poisson model precede analogous extensions to the

negative binomial. For example, statisticians have created random parameter and

random intercept count models to deal with certain types of correlated data. The first

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189

implementations were based on the Poisson distribution. In fact, negative binomial

models have been extended to account for a great many count-response modeling

situations.

Initial Estimation of Accident

Frequency by GLM Regression Model (Negative Binomial)

Number of Accidents Experienced at a Grade Crossing by Accident

History

Empirical Bayesian (EB) Model – Refined Estimation of Accident Frequency

Figure 5.9: Flow Diagram of Developing Empirical Bayesian (EB) Model

Grade crossing accidents are also direct measures of rail safety. The safety properties

of various crossing locations are clearly different. It is therefore evident that the

safety of a grade crossing can be evaluated on the basis of information from two

sources. The first source includes the railway geometric characteristics of locations

such as highway traffic volume, daily train movements, number of tracks, track

crossing angle, maximum timetable train speed, highway speed, etc. The second

source is obtained from the accident history of grade crossings. The combination of

two sources of safety information is facilitated in the development of the Empirical

Bayesian (EB) model approach as shown in the Figure 5.9. Hence, the EB model

provides a systematic refined estimation on accident frequency at a grade crossing.

An attempt was initiated to extend the negative binomial model in order to enhance

the quality of estimated accidents.

The results obtained from Negative Binomial regression models were refined by

applying the technique (as described above) called Empirical Bayesian (EB). As per

the EB equations shown below, the values of coefficient (κ ) and weights

( 1ω and 2ω ) were calculated. Finally, a combination of these values, estimated mean

values from the NB model ( )(ˆ YE ) and actual annual number of accidents from the

accident history (y) were used to predict the refined estimation of accidents (),(ˆ yYE ).

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)(ˆ*2*1),(ˆ YEyyYE ωω += (5.22)

2)](ˆ[

2)(ˆ*)(),(YE

YEyyYVar +Κ

Κ+= (5.23)

where 1ω and 2ω are the weighting factors used to determine the refined estimation

of accidents by linear combination of )(ˆ YE and y. The weighting factors are given by:

)](ˆ[

)(ˆ

1 YE

YE

+Κ=ω (5.24)

)](ˆ[2 YE+ΚΚ=ω

(5.25)

and therefore:

121 =+ωω (5.26)

Hauer, Ng and Lovell (1988) and Persaud and Dzbik (1993) have proved that for the

negative binomial model error structure, a parabolic relationship exists between

)(ˆ YE and )(YVar and κ is the parameter that describes this relationship by:

)(

2)(ˆ

YVar

YE=Κ (5.27)

5.3 Common Models of Accide ntal Consequences Prediction

It was noted that a number of statistical methods for predicting road collision severity

or consequence have been documented. Nassar, Saccomanno and Shortreed (1994)

proposed a series of sequential, nested logit models to predict occupant injury

severity for road collisions. Three classes of explanatory factors were considered:

physical (energy dissipation), driver condition and action, and occupant passive

response (e.g. wearing a seat belt, seating location in vehicle). Since the Nassar

model is occupant-specific, the severity of a given collision requires the summation

of the severity experienced by all occupants of all vehicles involved. Some studies

suggest using log-linear regression models rather than logit models to predict road

collision severity. It is argued that logit models do not provide a systematic means of

considering interactions among the various independent risk factors. Chen (1999)

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adopts a log-linear model to investigate the risk factors affecting bus driver injury

severity, and finds significant interaction effects between collision fault, time of

collision, and collision type affected severity. It is noted that different levels of

severity might be aggregated into a single combined value, which can be linked with

risk factors for predicting overall collision consequence at a given location or grade

crossing. However, limited research has been carried out in the past on various types

of models for predicting accident consequences (Highway-Railway Grade Crossing

Research: Identifying Black-Spots, Phase-1, University of Waterloo 2003).

5.3.1 Consequence Model by US Department of Transportation

Fatalities and casualties were the two stages of severity considered (Farr, E.H., 1987)

in the development of consequences models for railway-highway grade crossings by

the US Department of Transportation (USDOT). Fatal collisions are defined as

collisions that result in at least one fatality, while casualty collisions are defined as

collisions that result in either at least one fatality or injury. Both types of collisions

are reported in the Federal Railway Administration (FRA) occurrence databases. As

considered in the model, fatal collisions are a sub-set of casualty collisions. In the

USDOT consequence model the probability of a fatal collision (FA) given the prior

occurrence of a collision (C) is expressed as:

UR]* TS * TT * MS * KF [1

1C)|P(FA +=

(5.28)

where:

KF = 440.9; MS = 0.9981ms− ;

TT = 0.08721)(tt −+ ;

TS = 0.08721)(ts+

UR = ur0.3571e ;

ms = maximum timetable train speed;

tt = through trains per day

ts = switch trains per day; and

ur = urban / rural crossing (0 for rural and 1 for urban)

The probability of a casualty collision (CA) given a collision is expressed as:

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UR]*TK * MS * KC [1

1C)|P(CA +=

(5.29)

where:

KC = 4.481;

MS = 3430.ms− ;

TK = tk0.1153e− ;

UR = ur0.3571e ; and

tk = total number of tracks

The expected number of fatal and casualty collisions per crossing was obtained by

multiplying the expected number of collisions by the conditional probability of a

fatal or casualty collision, such that:

C)|P(FC * E[C] = (FA) E (5.30)

C)|P(CA * E[C] = (CA) E (5.31)

It should be noted that the USDOT consequence model does not take into account

the type of warning device found at a given crossing. Moreover, the model treats all

fatal collisions in a similar fashion regardless of number of fatalities incurred. The

USDOT consequence model focuses on the likelihood of a fatal and/or casualty

collision, not the numbers of fatalities or casualties associated with each collision.

This limits its use in distinguishing differences in severity among different collisions

at a given crossing.

5.3.2 Consequence Model by Canada Transport Development

Centre

Fatalities and personal injuries were observed to be a very small subset of total

crossing collisions in the Canadian data. The Transport Development Centre (TDC)

adopted a combined model that reflects the total consequence of a given collision

rather than developing separate models for each type of casualty as per the USDOT

approach. The total consequence is expressed in terms of a collision “severity score”,

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defined as the weighted sum of different types of consequence. This approach has

several advantages:

• It considers both fatalities and injuries in single expression rendering that is

easier to use in black-spots identification;

• It makes better use of crossing data - all crossings with collisions are

considered, not just those with casualties or fatalities; and

• It accounts for co-linearity between fatalities and personal injuries, so that

nesting the models is not required, as in USDOT expressions.

The consequence model developed for the identification of black-spots was:

TSPD)] * 0.0250 TA * 0.0069 TN * 0.2262 - PI * 0.3426[

)|(ˆ ++= eCqCE (5.32)

where:

C)|q

(CE = Expected consequence/collision

PI = Number of persons involved

TN = Number of railway tracks (both directions)

TA = Track angle (degrees)

TSPD = Maximum train speed (mph)

5.4 Major Steps in the Process of Model Development

The objective of modeling was to relate the average five-year accident frequency at

the grade crossings to the best set of explanatory variables. Sawatha & Sayad (2003)

stated that accident prediction models are invaluable tools that have some

applications in rail-road crossing safety analysis. Statistical modeling is used to

develop accident prediction models relating accident occurrence on various rail and

road facilities to the traffic and geometric characteristics of these facilities. These

models have applications such as estimation of the safety potential of rail-road

crossing entities, identification and ranking of hazardous or accident-prone locations,

evaluation of the effectiveness of safety improvement measures, and safety planning.

Currently, generalized linear modeling (GLM) is used almost exclusively for the

development of accident prediction models, since several researchers (e.g. Miaou &

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194

Lum 1993; Jovanis & Chang 1986) have demonstrated that certain standard

conditions under which conventional linear regression modeling is appropriate

(Normal error structure and constant error variance) are violated by traffic accident

data. The road safety literature is rich with accident prediction models relating

developed by Poisson or negative binomial regression. This means most safety

researchers now adopt either a Poisson or a negative binomial error structure in the

development of these models.

Several GLM statistical software packages are available for the development of these

models. This software allows the modeling of data that follow a wide range of

probability distributions belonging to the exponential family (among which are the

Poisson and the negative binomial distributions). A multiple regression approach was

therefore adopted within the framework of GLMs. The main advantage in doing this

is that the theory of GLMs allows the variation in the dependent variable to be

separated into the systematic and random parts (McCullagh & Nelder 1989). As a

consequence, it is possible to make structural and distributional assumptions, which

describe these two types of variations respectively (Kulmala 1995). The structural

assumption indicates that the expected value of the response variable can be related

through a “link function” to a set of explanatory variables and their coefficients. For

example, Poisson regression is one form of the Generalized Linear Model. In Poisson

regression, the response variable is modeled as a Poisson random variable with the

log link function.

On the other hand, random variation is described by a “random error term”

associated with the model, which reflects the distributional properties of the response

variable. The ordinary linear model tackles both the distributional and structural

assumptions together and assumes the response variable to be Normally-distributed,

quantitative and continuous and capable of taking any values. These run counter to

the basic properties of accident counts, which are discrete, non-negative and

generally governed by a non-stationary Poisson process (Jovanis & Chang 1986).

As indicated in the previous chapter, total records of 209,975 grade crossings in the

USA were utilised for the purpose of developing accident prediction models relating

the safety of rail-road crossing to their traffic and geometric characteristics. This total

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195

comprises four different protection types (depending on the nature of crossings) as

shown below.

• Crossing Protection Type 1 (No Signs or No Signals) - 11,274 records

• Crossing Protection Type 2 (Stop Signs or Cross-bucks) - 117,307 records

• Crossing Protection Type 3 (Signals, Bells or Warning Devices) - 39,397

records

• Crossing Protection Type 4 (Gates or Full Barriers) - 41,997 records

The data on accident frequencies were obtained from USDOT FRA Railway

Crossings Accident Database and covered the period from 2001 to 2005. Traffic and

geometric data were directly collected from USDOT FRA Railway Crossings

Inventory Database. The traffic data consisted of:

• Number of Daily Trains movement through each grade crossing;

• Annual Average of Daily Traffic (AADT) through each grade crossing;

• Maximum Train Speed; and

• Highway Speed;

The geometric data consisted of:

• Number of Main Tracks; and

• Number of Traffic Lanes.

In this study, SPSS (version 15) was used for accident prediction model

development. The following elements were necessary for model development

process:

• Appropriate functional form of model;

• Appropriate model distribution structure;

• Procedure for selecting the model explanatory variables;

• Procedure for building a Best-Fit model; and

• Methods for assessing model - goodness-of-fit.

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5.4.1 Functional Form of Model

The mathematical form of models used for predicting accidents should satisfy two

important conditions (Sawatha & Sayad 2003). Firstly, it must yield logical results.

This means that (a) it must not lead to the prediction of a negative number of

accidents and (b) it must ensure a prediction of zero accident frequency for zero

values of the exposure variables, which for rail-road crossings, are Number of Daily

Trains movement and annual average of daily traffic (AADT). The second condition

that must be satisfied by the model form is that, in order to use generalized linear

regression in the modeling procedure, there must exist a known link function that can

linearise this form for the purpose of coefficient estimation. These conditions are

satisfied by a model form that consists of the product of powers of the exposure

measures multiplied by an exponential incorporating the remaining explanatory

variables. Such a model form can be linearised by the logarithm link function.

Expressed mathematically, the model form that was used is as follows:

∑===ni

iiZid

ec

AADTb

DTaYE1

)*(

*)(*)(*)(ˆ (5.33)

where )(ˆ YE = predicted accident frequency; DT = daily train; AADT = annual average

daily traffic; iZ = any additional explanatory variable; and a , b , c & i

d = model

parameters. This form of equation satisfies the above-mentioned two conditions and

can be re-written as:

∑== +++=

ni

iiZidAADTLncDTLnbA

eYE1

)*)(*)(*(

)(ˆ (5.34)

or:

∑==+++= ni

iiZidAADTLncDTLnbAYELn

1*)(*)(*)](ˆ[

(5.35)

where;

)(aLnA = ; and eLogLn =

By specifying the dependent variable, the model form, error distribution (in this case

Poisson or Negative Binomial), the potential explanatory variables and the link

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function, the model is fitted, as the coefficients (model parameters) of the specified

variables are estimated using the method of maximum likelihood.

5.4.2 Model Distribution Structure

Traffic accident frequency can mathematically be modeled by a number of different

model distribution structures. Some of the distributions are Poisson, Gamma,

Negative Binomial and Empirical Bayesian etc. and these are explained in details

below.

5.4.2.1 Poisson Distribution

As mentioned earlier, the GLM approach to modeling traffic accident occurrence

assumes a distribution structure that is Poisson or negative binomial. Let Y be the

random variable that represents the accident frequency at a given location during a

specific time period, and let y be a certain realization of Y. The mean of Y, denoted

byΛ , is itself a random variable (Kulmala 1995). For λ=Λ , Y is Poisson distributed

with parameterλ :

y / = ) = |y = P(Y )(ye λλλ −Λ

(5.36)

λλ = ) = | E(Y Λ (5.37)

λλ = ) = | Var(Y Λ (5.38)

5.4.2.2 Gamma Distribution

It is the usual practice to assume that the distribution of Λ can be described by a

gamma probability density function. Hauer (1997) examined many accident data sets

and the empirical evidence he obtained supported the gamma assumption for the

distribution of Λ . If Λ is described by a gamma distribution with shape parameter

κ and scale parameter μκ / , then its density function is:

)()/(1

)()/()( / = κλμκκλκμκλ Γ−−Λ ef (5.39)

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= )E( μΛ (5.40)

κμ /

2= )Var(Λ (5.41)

5.4.2.3 Negative Binomial Distribution

The distribution of Y around μ=Λ)(E is negative binomial (Hinde & Demétrio

1998; Hauer, Ng & Lovell 1988). Therefore, unconditionally:

y

y

yyY ⎟⎠

⎞⎜⎝⎛⎟⎠

⎞⎜⎝⎛

++Γ+Γ=

μκμκ

μκκ

κκ

!)(

)(= )P(

(5.42)

μ = E(Y) (5.43)

κμμ /

2 = Var(Y) + (5.44)

As shown by above equations, the variance of the accident frequency is generally

larger than its expected value reflecting the fact that accident data are generally over-

dispersed. The only exception is when ∞→κ , in which case the distribution of Λ is

concentrated at a point and the negative binomial distribution becomes identical to

the Poisson distribution. The decision on whether to use a Poisson or negative

binomial distribution structure was based on the following methodology. First, the

model parameters are estimated based on a Poisson distribution structure. Then, the

dispersion parameter ( dσ ) is calculated as follows:

)(

2

pn

Pearson

d −= χσ (5.45)

where n is the number of observations, p is the number of model parameters, and

2χPearson is defined as:

∑=−= n

i iYVar

iYEiyPearson

1 )(

2)](ˆ[2χ (5.46)

where iy is the observed number of accidents on grade crossing i, )(ˆiYE is the

predicted accident frequency for grade crossing i as obtained from the accident

prediction model, and )( iYVar is the variance of the accident frequency for grade

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crossing i . The dispersion parameter, dσ , is noted by McCullagh and Nelder (1989)

to be a useful statistic for assessing the amount of variation in the observed data. If

dσ turns out to be significantly greater than 1.0, then the data have greater dispersion

than is explained by the Poisson distribution, and a negative binomial regression

model is fitted to the data.

5.4.2.4 Empirical Bayesian

As mentioned earlier, a number of researchers (Hauer, E.; Ng, J.C.N.; Lovell, J.;

Bonneson, J.A.; and McCoy, P.T.) have suggested that the Empirical Bayesian model

provides a good solution for problems of data over-dispersion. The EB prediction

model was included in this study solely for the purposes of extension to the Poisson

or NB model. By recalling the above-mentioned equation )(ˆ**),(ˆ21

YEyyYE ωω += ,

the EB model provides an estimate of predicted accidents at individual crossings

[ ),(ˆ yYE ] based on both statistical values obtained from other models [ )(ˆ YE ] and

historical input [ y ]. The inclusion of historical input may reflect the zero accident

events in the observed data. As such, it is expected to give a better prediction results

than Poisson or NB models.

5.4.3 Selection of Explanatory Variables for a Best-Fit Model

There seems to be a belief among many safety researchers that the more variables in

an accident prediction model the better the model. Some researchers have even

reported models containing variables with highly insignificant parameters based on

the belief that such variables would still improve model prediction. Such variables

are hardly of any value for explaining the variability of the specific accident data

used in generating the model much less of any value for predicting accident

frequencies at new locations not used in the model development. Explanatory

variables that have statistically significant model parameters, on the other hand,

contribute to the explanation of the variability of the accident data, and their

inclusion in the model therefore improves its fit to this data. Nevertheless,

improvement of a model’s fit to the accident data is not enough justification for

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retaining a variable in the model. Sawatha and Sayad (2003) presented a paper

showing a detailed analysis of how to select which explanatory variables to include

in an accident prediction model. The procedure suggested in the paper for selecting

the explanatory variables to include in an accident prediction model depends on the

locations the safety of which is to be studied by the model. This means that if an

accident prediction model is to be used for studying the safety of the particular set of

locations used to develop it, then a more accurate study would result by using a

model that fits the accident data as closely as possible. This best-fit model is

achieved by including all the available statistically significant explanatory variables.

5.4.4 Procedures for Selecting Ap propriate Variables for a Model

Developing Best-Fit accident prediction models is a forward procedure by which the

variables are added to a model one by one. The development of such a model is

explained later in the upcoming Section 5.4.6. The decision on whether a variable

should be retained in the model is based on three criteria. The first criterion is to

identify any data quality issues such as missing records or outliers in the independent

/variables. In this analysis firstly the variables which have extremely higher data

quality issues are discarded. The second criterion is whether the t-ratio of its

estimated parameter (equal to the parameter estimate divided by its standard error or

equivalent to the Wald chi-square statistic) is significant at the 95% confidence level.

This means that the minimum value of t-ratio should be at least 1.96 (equivalent

Wald chi-square is 3.841). The third criterion is whether the addition of the variable

to the model causes a significant drop in the scaled deviance at the 95% confidence

level. This criterion represents an analysis of deviance procedure for comparing two

nested models. This procedure is equivalent to carrying out a likelihood ratio test to

determine whether the model containing the additional variable significantly

increases the likelihood of the observed sample of accident data. The scaled deviance

is asymptotically2χ distributed with (n-p) degrees of freedom, and therefore, owing to

the reproductive property of the 2χ distribution, this second criterion is met if the

addition of the variable causes a drop in scaled deviance exceeding2

1,05.0χ which is

equal to 3.841 (Maycock & Hall 1984).

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5.4.5 Assessment of Final Model for Goodn ess-of-Fit

Several statistical measures can be used to assess the goodness-of-fit of GLM

models. The two common statistical measures used are those cited by McCullagh and

Nelder (1989) for assessing goodness-of-fit of accidents predicting models. These

are:

• Pearson2χ statistic; or

• Scaled deviance.

However, Wood (2002) and Maher and Summersgill (1996) argue that the 2χPearson

statistic should be used to evaluate the model adequacy when the mean is low (values

less than 0.5). In this study, as the analysis shows the mean value of accident

frequency for any type of crossings found to be far less than 0.5, the 2χPearson

statistic is used to evaluate the model adequacy. Both the scaled deviance and

2χPearson have 2χ distributions for Normal theory linear models, but they are

asymptotically 2χ distributed with (n-p) degrees of freedom for other distributions of

exponential family.

R-Square (R2), also known as the Coefficient of determination, is a commonly used

statistic to evaluate model fit. R-square is 1 minus the ratio of residual variability.

When the variability of the residual values around the regression line relative to the

overall variability is small, the predictions from the regression equation are good. For

example, if we have an R-square of 0.35 then we know that the variability of the

residual values around the regression line is (1- 0.35) times the original variance; in

other words we have explained 35% of the original variability, and are left with 65%

residual variability. Ideally, we would like to explain most if not all of the original

variability. The R-square value is an indicator of how well the model fits the data

(e.g., an R-square close to 1.0 indicates that we have accounted for almost all of the

variability with the variables specified in the model). In this study 0.35 has been

selected as the minimum value of R2 for best-fit models.

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5.4.6 Procedures for Selecting Final Model

The major four steps involved in the procedures for selecting the appropriate final

model are explained below. Basically, development of accident prediction models is

a forward procedure by which the explanatory variables are added to a model one by

one until the final best-fit model is obtained. The steps involved in such procedures

were explained early in the Section 5.4.4.

5.4.6.1 Step-1: Developing a GLM Poisson Regression Model

As indicated in the Section 4.1.1.2, by considering and overcoming data quality

issues, seven appropriate explanatory variables (Daily Train Traffic, Annual Average

Daily Traffic, Train Speed, Highway Vehicles Speed, Track Crossing Angle,

Number of Main Tracks, and Number of Traffic Lanes) from the USDOT inventory

database are used in developing the accident prediction models in this study. Firstly,

a very basic GLM Poisson Regression model, which contains only two exposure

variables (Daily Train Traffic and Annual Average Daily Traffic) is generated in

SPSS V15. This is known as the Reference Poisson Model for accidents prediction.

The remaining five variables are added to the model one by one according to the

procedures explained in the Section 5.4.4 and all appropriate variables are then

identified to fit in the Poisson Regression model. The flow chart of these procedures

is depicted in Figure 5.10.

5.4.6.2 Step-2: Developing a GLM Negative Binomial Regression Model

The same procedure explained in Step-1 is repeated with Negative Binomial

Regression model for accidents prediction instead of Poisson model. All appropriate

variables are then identified to fit in the NB Regression model. The flow chart of

these procedures is depicted in Figure 5.11.

5.4.6.3 Step-3: Selection of Appropriate Model - Poisson or Negative Binomial

This step involves comparing the Negative Binomial model with the Poisson model

which are developed in the previous steps (1 and 2), and testing the goodness-of-fit

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values of those models. The first test for goodness-of-fit is the value of Pearson2χ .

Pearson 2χ statistic follows the

2χ distribution with the number of degrees of

freedom and therefore for a well-fitted model, the expected value of Pearson

2χ should be approximately equal to the number of degrees of freedom. In other

words, the well-fitted model should yield a Pearson 2χ (per the number of degrees

of freedom) value of 1 approximately. The next test for goodness-of-fit is the

estimation of Akaike's Information Criterion (AIC) value. The well-fitted model is

indicated by the lowest value of AIC. Based on these criteria, the well-fitted model

(either Poisson or NB) is selected in the initial process of accidents prediction. The

flow chart of these procedures is depicted in Figure 5.12.

5.4.6.4 Step-4: Utilising Empirical Bayesian Models

An Empirical Bayesian model is finally developed in order to enhance the quality of

accident prediction with adjustment to the better-fit model selected in Step-3. In

order to select the final best-fit model a Chi-square goodness-of-fit test was

separately applied to the test results obtained by the better-fit model selected in Step-

3 and EB models for each of the explanatory variables. In comparing the calculated

Chi-square values on both models, the model which shows the 2χ values are less

than the relevant critical values for all explanatory variables is selected as the final

best-fit model. In addition, the R2 value of the final best-fit model is also tested for an

indication of how well the model fits the data. In this study, 0.35 has been selected as

the minimum value of R2 for adequacy of models. The flow chart of these procedures

is depicted in Figure 5.13.

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Add explanatory variable (i

Z , where i =

1,2,….n) to the Reference Model

Is t-Ratio of i

Z

significant ? (p < 0.05)

If i

Z added, is drop

in SD significant? (Drop in SD > 3.841)

Build the Model with all appropriate

explanatory variables

Can the Model pass Goodness of Fit test ( 2χPearson statistic

or Scaled Deviance)

Reject Poisson Model

Start with GLM Poisson Regression Model in SPSS (V 15) Generate a very basic GLM model, which contains only

exposure variables (Daily Train Traffic and AADT). This is known as the Reference Poisson Model.

Accept Better-Fit Poisson Model

Discard i

Z and Try with 1+iZ

Discard i

Z and Try

with 1+iZ

Can other independent variables be identified after fixing data quality issues

such as missing records or outliers.

Discard variables with highly affected by data quality

issues or correlation

Figure 5.10: Flow Diagram of Better-Fit Poisson Model Building Process (Step 1)

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Add explanatory variable (i

Z , where i =

1,2,….n) to the Reference Model

Is t-Ratio of i

Z

significant ? (p < 0.05)

If i

Z added, is drop

in SD significant? (Drop in SD > 3.841)

Build the Model with all appropriate

explanatory variables

Can the Model pass Goodness of Fit test ( 2χPearson statistic

or Scaled Deviance)

Reject NB Model

Start with GLM NB Regression Model in SPSS (V 15) Generate a very basic GLM model, which contains only

exposure variables (Daily Train Traffic and AADT). This is known as the Reference Negative Binomial Model.

Accept Better-Fit NB Model

Discard i

Z and Try with 1+iZ

Discard i

Z and Try

with 1+iZ

Can other independent variables be identified after fixing data quality issues

such as missing records or outliers.

Discard variables with highly affected by data quality

issues or correlation

Figure 5.11: Flow Diagram of Better-Fit Negative Binomial Model Building Process (Step 2)

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Better-Fit NB Model Obtained by Step 2

Compare Poisson and NB Models and conduct Goodness-of-Fit Test by testing: • Pearson Chi-Square value per degrees of

freedom; and • Akaike's Information Criterion (AIC) value

Select the Final Better-Fit Model

(Either Poisson or NB)

Better-Fit Poisson Model Obtained by Step 1

Figure 5.12: Flow Diagram of Comparing Poisson and NB Models (Step 3)

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Estimation of Accident Frequency from Final Better-Fit Model accepted in Model

Building Step 3 [ )(ˆ YE ]

Number of Accidents Experienced at a Grade Crossing in Accident History

[ y ]

Build Empirical Bayesian (EB) Model – Refined Estimation of

Accident Frequency

[ )(ˆ**),(ˆ21

YEyyYE ωω += ]

Can the Model pass Goodness of Fit test on

each explanatory variable? (Pearson Chi-Square

2

,05.0

2

γχχ ≤ )

Is Estimated Coefficient of Determination

35.0)(2 ≥R

Accept Final (Best-Fit) EB Model

Accept Better-Fit Model Obtained

From Model Building Step 3 (Either Poisson or NB)

Figure 5.13: Flow Diagram of Best-Fit EB Model Building Process (Step 4)

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5.5 Results on Models Developed for Each Protection Type

As indicated earlier, the SPSS (Version 15) package was used in this study for

developing both accident frequency and accidental consequence prediction models

for each of the four protection types of grade crossings. The forms of the Poisson and

Negative Binomial models are found in GLM command procedure in SPSS V15.

Both predictions are initially estimated based on GLM. The results are then examined

and discussed in order to assess the adequacy of the both models. By comparison, the

better prediction model is selected. Applying the technique called Empirical

Bayesian (EB) as discussed earlier refines the estimation obtained from the better

model. Finally, the EB model is tested for goodness-of-fit and selected as the best

model for prediction.

Adequacy of models

In order to assess the adequacy of these models, basic descriptive statistics for event

count data were examined. If the count mean and variance are very different

(equivalent in a Poisson distribution) then the model is likely to be over-dispersed.

The Pearson correlation between each variable was checked for existence of high

values. The t-ratios of the parameter estimates of both models were also tested for

significance level at 5%. The scaled deviance at the 95 % confidence level was also

checked for significance when adding each variable to the model. The GLM model

analysis option gives a scale parameter as a measure of over-dispersion of models.

This is equal to the scaled Pearson Chi-square statistic divided by the number of

observations minus the number of parameters (covariates and intercept). The

variances of the coefficients can be adjusted by multiplying scale parameter. The

goodness-of -it test statistics and residuals can be adjusted by dividing by scale

parameter. A better approach to over-dispersed Poisson models is to use a parametric

alternative model, Negative binomial. All finalised models were tested on values of

determination coefficient ( 2R ) and of Pearson2χ that are significant at the 95%

confidence level indicating that the models have an acceptable fit to the data.

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5.5.1 Generating Models Pred icting Accident Frequencies

As described above, for developing best-fit accident predictions models the methods

and procedures were used to develop such models for the grade crossings in the

USA. The procedures were initiated by developing a Poisson model, followed by

building a Negative Binomial (NB) model. Finally an Empirical Bayesian (EB)

model was developed to give a better prediction result by including historical data.

All models (predicting total accident frequency in a period of five years) were

individually developed and listed below for each of the four distinctive protection

types of grade crossings. The dependent variable used in models development is

Number of Total Accidents (NTA) for a public grade crossing in the five-year period

(2001-2005). As discussed in the Section 4.1.1.2 of Chapter 4, only seven

independent variables are used at the stage of model development for accident

frequency prediction. All steps involved in the filtering process of identifying

appropriate variables (from the USDOT inventory database) prior to developing final

risk assessment model using statistical methods were earlier shown in Table 4.1.

Following are the seven selected independent variables used in the models and their

abbreviations:

• Daily Train Movement (DT)

• Annual Average Daily Traffic (AADT)

• Maximum Timetable Train Speed (MTTS)

• Highway Speed (HS)

• Number of Main Tracks (MT)

• Number of Traffic Lanes (TL)

• Track Crossing Angle (TCA)

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5.5.1.1 Crossing Protection Type 1 (No Signs or No signals)

In the Protection Type 1 group, a total of 91 accidents were reported during the 2001-

2005 period in the USA. In this group, only 84 crossings (0.75%) out of 11,274

crossings experienced accidents. This means that the data contains several zero-

accident occurrences. This tendency presents problems in predicting the accidents at

grade crossings using the simple Poisson model. There are only 160 records

considered suitable for model development once the other records, which have data

quality issues with variables, have been discarded. The value of 3 was recorded for

the maximum number of accidents at a given crossing in this group. Descriptive

statistics of eight variables, which were considered to initiate the model development,

are summarised in Table 5.4.

Table 5.4: Descriptive Statistics on Variables Used in the Model - Protection Type 1

Crossing Protection Type 1 Count Minimum Maximum Mean Std. Deviation

Number of Accidents in 5 Years 160 0 3 0.18 0.44

Daily Train Movement 160 2 183 9.04 15.16

Annual Average Daily Traffic 160 11 22925 653.55 2450.52

Maximum Timetable Train Speed 160 1 79 20.95 11.84

Highway Speed 160 0 55 1.22 6.72

Number of Main Tracks 160 0 2 0.73 0.56

Number of Traffic Lanes 160 1 4 1.64 0.69

Track Crossing Angle 160 1 3 2.79 0.53

In the early part of modeling analysis in this group, Pearson correlation values for the

independent variables were estimated and shown in Table 5.5. As these variables

show reasonably low values in correlation, all of them were initially selected in the

process of model development.

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Table 5.5: Pearson Correlation Between Variables Used in the Model - Protection Type 1

Crossing Protection Type 1

Daily Train

Movement

Annual

Average

Daily Traffic

Maximum

Timetable

Train Speed

Highway

Speed

Number of

Main Tracks

Number of

Traffic

Lanes

Track

Crossing

Angle

Daily Train Movement 1.00 0.01 0.04 -0.04 0.03 -0.05 0.03

Annual Average Daily Traffic 0.01 1.00 -0.05 0.08 0.08 0.37 0.05

Maximum Timetable Train

Speed 0.04 -0.05 1.00 -0.05 0.32 -0.06 -0.07

Highway Speed -0.04 0.08 -0.05 1.00 0.06 0.10 0.01

Number of Main Tracks 0.03 0.08 0.32 0.06 1.00 -0.07 0.06

Number of Traffic Lanes -0.05 0.37 -0.06 0.10 -0.07 1.00 0.06

Track Crossing Angle 0.03 0.05 -0.07 0.01 0.06 0.06 1.00

a. GLM Poisson Regression Model

For the Poisson model, seven independent variables were initially investigated. Two

of the seven variables (annual average daily traffic and maximum timetable train

speed) were found to be statistically significant at 5% level (Table 5.6). The

discarded variables were daily train movement, highway speed, number of main

tracks, number of traffic lanes and track crossing angle, as their significance values

showed more than 0.05. Table 5.7 shows the goodness-of-fit details on the GLM

Poisson Regression model.

Table 5.6: Parameter Estimates of GLM Poisson Regression Model - Protection Type 1

Parameter B Std. Error

95% Wald Confidence

Interval Hypothesis Test

Lower Upper Wald Chi-Square df Sig.

(Intercept) -5.757 0.717 -7.163 -4.351 64.418 1 0.000

MTTS 0.024 0.011 0.002 0.045 4.784 1 0.029

Ln (AADT) 0.614 0.089 0.440 0.788 47.823 1 0.000

(Scale) a

1

Dependent Variable: NTA

Model: (Intercept), MTTS, Ln (AADT)

a - Fixed at the displayed value.

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Table 5.7: Goodness-of-Fit Results of GLM Poisson Regression Model - Protection Type 1

Crossing Protection Type 1 Value df Value / df

Deviance 60.0 157 0.382

Scaled Deviance 60.0 157

Pearson Chi-Square 210.2 157 1.339

Scaled Pearson Chi-Square 210.2 157

Log Likelihood(a) -59.8

Akaike's Information Criterion (AIC) 125.6

Finite Sample Corrected AIC (AICC) 125.8

Bayesian Information Criterion (BIC) 126.9

Consistent AIC (CAIC) 129.9

Dependent Variable: NTA

Model: (Intercept), MTTS, Ln (AADT)

Accident Predic t ion Equat ion from GLM Model (Poisso n Regression)

According to results obtained from the Poisson model, the expected number of

accidents per 5 years at each crossing is expressed as:

(AADT)]Ln *0.614 MTTS * 0.024 -5.757[1)(ˆ ++= eGYE (5.47)

where 1)(ˆ

GYE - Number of accidents expected to occur at a crossing in Group1 in 5

years.

b. GLM Negat ive Binomia l Regression Model

The Negative Binomial model reflects on the same explanatory variables, which

were selected for the above-mentioned Poisson model. However, the parameter

estimation values on these variables in the NB model show a slight difference from

the Poisson model (Table 5.8). Table 5.9 shows the goodness-of-fit details on the

GLM Negative Binomial Regression model.

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Table 5.8: Parameter Estimates of GLM Negative Binomial Model - Protection Type 1

Parameter B Std. Error

95% Wald Confidence

Interval Hypothesis Test

Lower Upper Wald Chi-Square df Sig.

(Intercept) -6.369 0.875 -8.085 -4.653 52.940 1 0.000

MTTS 0.030 0.015 0.001 0.058 4.164 1 0.041

Ln (AADT) 0.695 0.115 0.469 0.921 36.343 1 0.000

(Scale) a

1

Dependent Variable: NTA

Model: (Intercept), MTTS, Ln (AADT)

a - Fixed at the displayed value

Table 5.9: Goodness-of-Fit Results of GLM Negative Binomial Model - Protection Type 1

Crossing Protection Type 1 Value df Value / df

Deviance 46.7 157 0.298

Scaled Deviance 46.7 157

Pearson Chi-Square 205.2 157 1.307

Scaled Pearson Chi-Square 205.2 157

Log Likelihood(a) -50.4

Akaike's Information Criterion (AIC) 124.8

Finite Sample Corrected AIC (AICC) 125.0

Bayesian Information Criterion (BIC) 134.1

Consistent AIC (CAIC) 137.1

Dependent Variable: NTA

Model: (Intercept), MTTS, Ln (AADT)

Accident Predic t ion Equat ion from GL M Model (Negat ive Binomia l Regression)

According to results obtained from the NB model, the expected number of accidents

per 5 years at each crossing in this group is expressed as:

(AADT)]Ln *0.695 MTTS * 0.030 -6.369[

1)(ˆ ++= eGYE (5.48)

where: 1)(ˆ

GYE - Number of accidents expected to occur at a crossing in Group1 in 5

years.

Goodness-of-Fit Results and Comparisons betw een Poiss on and NB Models

By referring the goodness-of-fit values, the Poisson model yielded a Pearson Chi-

Square (value per degrees of freedom) to 1.339 suggesting a minor amount of over-

dispersion in the data (Table 5.7). The Negative Binomial model (Table 5.9) shows a

slightly better result in Pearson Chi-Square value (1.307). In comparison to the

Akaike's Information Criterion (AIC) the value of the NB model (124.8) is slightly

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smaller than that of the Poisson model (125.6). In addition, the values for mean and

variance of the accident count data for Protection Type 1 crossings show 0.18 and

0.19 respectively. Since the Poisson model requires the mean and variance to be

equal, it is unsuitable for data with greater variance than mean. The Negative

Binomial may be more appropriate in such settings as its variance is always larger

than the mean. Based on these findings, the NB model is therefore considered to be

more appropriate than the Poisson model in the initial process of accidents

prediction. The Empirical Bayesian model is then used with adjustment to the NB

model developed in order to enhance the quality of prediction.

c. Empirica l Bayesian Model (Adjustm ent to GLM NB Regression Model

Results)

In accordance with the equations 5.24, 5.25 and 5.27, the weighting factors (1ω and

2ω ) and the over-dispersion parameter (κ ) for the Protection Type 1 crossings were

calculated and are shown in Table 5.10.

Table 5.10: Over-Dispersion Parameter and Weighting Factors Estimation - EB Model

Crossing Protection Type 1

Mean of Accidents Estimated by NB Model - )(ˆ YE 0.1750

Variance of Accidents - )(YVar 0.1956

Over-Dispersion Parameter - κ 0.1566

Weighting Factor - 1ω 0.5579

Weighting Factor - 2ω 0.4421

Acc ident Predic t ion Equat ion from EB Model

The EB model prediction based on the adjustment to the NB model results shows that

the expected number of accidents per 5 years at each crossing in the Protection

Type 1 is expressed as:

1)(ˆ*2*11),(ˆGYEyGyYE ωω += (5.49)

or:

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(AADT)]Ln *0.695 MTTS * 0.030 -6.369[

*4421.0*5579.01),(ˆ +++= eyGyYE (5.50)

where 1),(ˆ

GyYE - Number of accidents (predicted by EB Model) expected to occur at a

crossing in Group1 in 5 years.

Comparison of Goodness-of-Fit Results betw een EB and NB Models for Fina l

Select ion

A Chi-square goodness-of-fit test was separately applied to the test results obtained

by the NB and EB models for each of the explanatory variables. The Chi-square

goodness-of-fit values for Maximum timetable train speed and Annual average daily

traffic are calculated and shown in Tables 5.11 and 5.12 respectively. For these

explanatory variables the calculated Chi-square values on the NB model showed 6.51

and 7.88 respectively. The values on the EB model showed 1.06 and 1.64

respectively. These results show that both models have Chi-square values less than

the critical value (2

4,05.0χ = 9.49) at 5% level of significance. However, in comparison

to calculated Chi-square values, the EB model shows a better result than the NB

model in all cases. In addition, the EB model estimates the R-square (R2) value of

0.79. This means that the model has explained 79% of the original variability, and is

left with 21% residual variability. In summary, even though this group of crossings

(with No Signs or No signals) suggested a minor problem of over-dispersion in the

accidents data, the EB model is more statistically acceptable for prediction of

accidents.

Table 5.11: Goodness-of-Fit Results of NB & EB Models - Max Timetable Train Speed

Maximum Time Table Train Speed

(mph)

Number of Observed

Accidents Used in Developing

Models

Predicted Frequency of Accidents for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

1_10 9 10.27 9.56 0.16 0.03

11_20 2 3.71 2.76 0.79 0.21

21_25 6 2.66 4.52 4.20 0.48

26_35 4 6.89 5.28 1.21 0.31

Over 35 7 8.08 7.48 0.14 0.03

Grand Total 28 31.62 29.60 6.51 1.06

Critical Chi-Square Value ( 24,05.0χ ) 9.49 9.49

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Table 5.12: Goodness-of-Fit Results of NB & EB Models - Annual Average Daily Traffic

Annual Average of Daily Traffic (vehicles)

Number of Observed

Accidents Used in Developing

Models

Predicted Frequency of Accidents for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

101_250 6 8.53 7.12 0.75 0.18

251_1000 7 3.93 5.64 2.41 0.33

1001_1500 4 3.52 3.79 0.07 0.01

1501_5000 5 3.07 4.15 1.22 0.18

Over 5000 6 12.57 8.91 3.44 0.95

Grand Total 28 31.62 29.60 7.88 1.64

Critical Chi-Square Value ( 24,05.0χ ) 9.49 9.49

Specific Calcula t ions for Acc idents Predi c t ion at Grade Crossings using EB Model

Consider the crossing (ID No: 731580L) with the historical data of one (1) accident

in the period 2001-2005; maximum timetable train speed (55); and annual average

daily traffic (1000). Using the Equation 5.48, the NB model predicts the number of

accidents at this grade crossing in the five-year period as:

=++= (1000)]Ln *0.695 55 * 0.030 -6.369[)(ˆ

731580e

LYE 1.07

From Table 5.10, the values of weighting factors are: =1ω 0.5579 and =2ω 0.4421. Using

the Equation 5.49, the EB model predicts the number of accidents at this grade

crossing in the five-year period as:

=+= 07.1*4421.01*5579.0),(ˆ731580L

yYE 1.03

Similarly, the number of accidents was estimated for crossing in the group using the

NB and EB models and the relevant values were recorded. For example, Table 5.13

reveals the top ten accidental crossings predicted by EB model in the group.

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Table 5.13: Top Ten Accidental Locations by EB Model Prediction in Protection Type 1

Grade Crossing

ID

Number of Accidents in

History (5 Years)

Prediction of Accidents Using

NB Model (5 Years)

Prediction of Accidents Using EB

Model (5 Years)

625789S 1 3.21 1.98

022694S 1 2.78 1.78

756003K 3 0.19 1.76

326937J 1 2.48 1.65

632469J 1 1.96 1.42

347216S 1 1.47 1.21

026334H 1 1.39 1.17

231621H 2 0.03 1.13

626426C 1 1.24 1.11

731580L 1 1.07 1.03

5.5.1.2 Crossing Protection Type 2 (Stop Signs or Cross-bucks)

A total of 4,743 accidents in the Protection Type 2 were reported during the 2001-

2005 period in the USA. In this group, only 3,998 crossings (3.41%) out of 117,306

crossings experienced accidents. This shows the data are dominant with zero-

accident occurrences. This tendency presents problems in predicting accidents at

grade crossings in using the simple Poisson model. There are only 6,288 records

considered suitable for model development once the other records, which have data

quality issues with variables, have been discarded. The value of 9 was recorded for

the maximum number of accidents at a given crossing in this group. Descriptive

statistics of eight variables, which were considered to initiate the model development,

are summarised in Table 5.14.

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Table 5.14: Descriptive Statistics on Variables Used in the Model - Protection Type 2

Crossing Protection Type 2 Count Minimum Maximum Mean Std. Deviation

Number of Accidents in 5 Years 6288 0 9 0.18 0.47

Daily Train Movement 6288 1 158 7.38 9.54

Annual Average Daily Traffic 6288 1 36680 706.59 1503.09

Maximum Timetable Train Speed 6288 1 80 30.63 17.24

Highway Speed 6288 5 65 34.50 12.26

Number of Main Tracks 6288 0 3 0.92 0.36

Number of Traffic Lanes 6288 1 6 1.89 0.34

Track Crossing Angle 6288 1 3 2.75 0.51

In the early part of modeling analysis in this group, Pearson correlation values for the

independent variables were estimated and shown in Table 5.15. As these variables

show reasonably low values in correlation, all of them were initially selected in the

process of model development.

Table 5.15: Pearson Correlation Between Variables Used in the Model - Protection Type 2

Crossing Protection Type 2

Daily Train

Movement

Annual

Average

Daily Traffic

Maximum

Timetable

Train Speed

Highway

Speed

Number of

Main Tracks

Number of

Traffic

Lanes

Track

Crossing

Angle

Daily Train Movement 1.00 -0.11 0.55 -0.07 0.27 -0.16 0.09

Annual Average Daily Traffic -0.11 1.00 -0.23 -0.06 -0.19 0.21 -0.05

Maximum Timetable Train

Speed 0.55 -0.23 1.00 0.11 0.37 -0.19 0.10

Highway Speed -0.07 -0.06 0.11 1.00 0.07 0.18 -0.05

Number of Main Tracks 0.27 -0.19 0.37 0.07 1.00 -0.11 0.14

Number of Traffic Lanes -0.16 0.21 -0.19 0.18 -0.11 1.00 -0.02

Track Crossing Angle 0.09 -0.05 0.10 -0.05 0.14 -0.02 1.00

a. GLM Poisson Regression Model

For the Poisson model, seven independent variables were initially investigated. Five

of the seven variables (daily train movement, annual average daily traffic, maximum

timetable train speed, highway speed and number of traffic lanes) were found to be

statistically significant at 5% level (Table 5.16). The discarded variables were

number of main tracks and track crossing angle as their significance values showed

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more than 0.05. Table 5.17 shows the goodness-of-fit details on the GLM Poisson

Regression model.

Table 5.16: Parameter Estimates of GLM Poisson Regression Model - Protection Type 2

Parameter B Std. Error

95% Wald Confidence

Interval Hypothesis Test

Lower Upper Wald Chi-Square df Sig.

(Intercept) -5.861 0.234 -6.319 -5.402 626.957 1 0.000

MTTS 0.014 0.002 0.009 0.018 39.620 1 0.000

HS 0.016 0.003 0.010 0.021 36.270 1 0.000

TL 0.301 0.090 0.124 0.478 11.113 1 0.001

Ln (DT) 0.505 0.035 0.436 0.574 205.518 1 0.000

Ln (AADT) 0.302 0.023 0.256 0.348 165.054 1 0.000

(Scale) a

1

Dependent Variable: NTA

Model: (Intercept), MTTS, HS, TL, Ln (DT), Ln (AADT)

a - Fixed at the displayed value.

Table 5.17: Goodness-of-Fit Detail of GLM Poisson Regression Model - Protection Type 2

Crossing Protection Type 1 Value df Value / df

Deviance 3824.7 6282 0.609

Scaled Deviance 3824.7 6282

Pearson Chi-Square 7018.9 6282 1.117

Scaled Pearson Chi-Square 7018.9 6282

Log Likelihood(a) -2976.3

Akaike's Information Criterion (AIC) 5964.6

Finite Sample Corrected AIC (AICC) 5964.6

Bayesian Information Criterion (BIC) 5985.0

Consistent AIC (CAIC) 5991.0

Dependent Variable: NTA

Model: (Intercept), MTTS, HS, TL, Ln (DT), Ln (AADT)

Accident Predic t ion Equat ion from GLM Model (Poisso n Regression)

According to results obtained from the Poisson model, the expected number of

accidents per 5 years at each crossing is expressed as:

(AADT)]Ln *0.302 (DT)Ln * 0.505 TL * 0.301HS * 0.016 MTTS * 0.014 -5.861[

2)(ˆ +++++= eGYE (5.51)

where 2)(ˆ

GYE - Number of accidents expected to occur at a crossing in Group2 in 5

years.

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b. GLM Negat ive Binomia l Regression Model

The Negative Binomial model reflects on the same explanatory variables, which

were selected for the above-mentioned Poisson model. However, the parameter

estimation values on these variables in the NB model show a slight difference from

the Poisson model (Table 5.18). Table 5.19 shows the goodness-of-fit details on the

GLM Negative Binomial Regression model.

Table 5.18: Parameter Estimates of GLM Negative Binomial Model - Protection Type 2

Parameter B Std. Error

95% Wald Confidence

Interval Hypothesis Test

Lower Upper Wald Chi-Square df Sig.

(Intercept) -5.822 0.273 -6.358 -5.286 453.986 1 0.000

MTTS 0.015 0.002 0.010 0.020 35.664 1 0.000

HS 0.014 0.003 0.008 0.020 22.868 1 0.000

TL 0.313 0.109 0.100 0.527 8.307 1 0.004

Ln (DT) 0.484 0.041 0.404 0.564 141.174 1 0.000

Ln (AADT) 0.300 0.027 0.247 0.352 125.050 1 0.000

(Scale) a

1

Dependent Variable: NTA

Model: (Intercept), MTTS, HS, TL, Ln (DT), Ln (AADT)

a - Fixed at the displayed value.

Table 5.19: Goodness-of-Fit Results of GLM Negative Binomial Model - Protection Type 2

Crossing Protection Type 1 Value df Value / df

Deviance 3043.1 6282 0.484

Scaled Deviance 3043.1 6282

Pearson Chi-Square 6026.6 6282 0.959

Scaled Pearson Chi-Square 6026.6 6282

Log Likelihood(a) -2971.2

Akaike's Information Criterion (AIC) 5954.5

Finite Sample Corrected AIC (AICC) 5954.5

Bayesian Information Criterion (BIC) 5995.0

Consistent AIC (CAIC) 6001.0

Dependent Variable: NTA

Model: (Intercept), MTTS, HS, TL, Ln (DT), Ln (AADT)

Accident Predic t ion Equat ion from GL M Model (Negat ive Binomia l Regression)

According to results obtained from the NB model, the expected number of accidents

per 5 years at each crossing in this group is expressed as:

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(AADT)]Ln *0.300 (DT)Ln * 0.484 TL * 0.313HS * 0.014 MTTS * 0.015 -5.822[2)(ˆ +++++= eGYE (5.52)

where: 2)(ˆ

GYE - Number of accidents expected to occur at a crossing in Group2 in 5

years.

Goodness-of-Fit Results and Comparisons betw een Poiss on and NB Models

By referring the goodness-of-fit values, the Poisson model yielded a Pearson Chi-

Square (value per degrees of freedom) to 1.117, suggesting a minor amount of over-

dispersion in the data (Table 5.17). The Negative Binomial model (Table 5.19) shows

a slightly better result in Pearson Chi-Square value (0.959). In comparison of the

Akaike's Information Criterion (AIC), the value of the NB model (5954.5) is slightly

smaller than that of the Poisson model (5964.6). In addition, the values for mean and

variance of the accident count data for Protection Type 2 crossings show 0.18 and

0.22 respectively. Since the Poisson model requires the mean and variance to be

equal, it is unsuitable for data with greater variance than mean. The Negative

Binomial may be more appropriate in such settings as its variance is always larger

than the mean. Based on these findings, the NB model is therefore considered to be

more appropriate than the Poisson model in the initial process of accidents

prediction. The Empirical Bayesian model is then used with adjustment to the NB

model developed in order to enhance the quality of prediction.

c. Empirica l Bayesian Model (Adjustm ent to GLM NB Regression Model

Results)

In accordance with the equations 5.24, 5.25 and 5.27, the weighting factors (1ω and

2ω ) and the over-dispersion parameter (κ ) for the Protection Type 2 crossings were

calculated and are shown in Table 5.20.

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Table 5.20: Over-Dispersion Parameter and Weighting Factors Estimation - EB Model

Crossing Protection Type 2

Mean of Accidents Estimated by NB Model - )(ˆ YE 0.1843

Variance of Accidents - )(YVar 0.2216

Over-Dispersion Parameter - κ 0.1533

Weighting Factor - 1ω 0.5453

Weighting Factor - 2ω 0.4547

Accident Predic t ion Equat ion from EB Model

The EB model prediction based on the adjustment to the NB model results shows that

the expected number of accidents per 5 years at each crossing in the Protection Type

2 is expressed as:

2)(ˆ*2*12),(ˆGYEyGyYE ωω += (5.53)

or:

(AADT)]Ln *0.300 (DT)Ln * 0.484 TL * 0.313HS * 0.014 MTTS * 0.015 -5.822[*4547.0*5453.02),(ˆ

++++++= eyGyYE

(5.54)

where 2),(ˆ

GyYE - Number of accidents (predicted by EB Model) expected to occur at a

crossing in Group2 in 5 years.

Comparison of Goodness-of-Fit Results betw een EB and NB Models for Fina l

Select ion

A Chi-square goodness-of-fit test was separately applied to the test results obtained

by the NB and EB models for each of the explanatory variables. The Chi-square

goodness-of-fit values for maximum timetable train speed, highway speed, number

of traffic lanes, daily train movement and annual average daily traffic are calculated

and shown in Tables 5.21, 5.22, 5.23, 5.24 and 5.25 respectively. For these

explanatory variables the calculated Chi-square values on the NB model showed

24.63, 40.94, 9.23, 7.64 and 18.82 respectively. However, only two of them are

found to be less than the critical value (2

4,05.0χ = 9.49) at the 5% level of significance.

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The calculated Chi-square values on the EB model showed 5.19, 8.88, 1.41, 1.48 and

4.08 respectively. All of these values are less than the critical value for the

explanatory variables. In comparison to calculated Chi-square values, the EB model

shows better result than the NB model in all cases. In addition, the EB model

estimates the R-square (R2) value of 0.37. This means that the model has explained

37% of the original variability, and is left with 63% residual variability. In summary,

even though this group of crossings (with Stop Signs or Cross-bucks) suggested a

minor problem of over-dispersion in the accidents data, the EB model is more

statistically acceptable for prediction of accidents.

Table 5.21: Goodness-of-Fit Results of NB & EB Models - Max Timetable Train Speed

Maximum Time Table Train Speed

(mph)

Number of Observed

Accidents Used in Developing

Models

Predicted Frequency of Accidents for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

1_20 261 232.42 248.00 3.51 0.68

21_30 201 252.45 224.40 10.49 2.44

31_40 216 206.63 211.74 0.43 0.09

41_50 253 212.11 234.40 7.88 1.48

Over 50 228 252.18 239.00 2.32 0.51

Grand Total 1159 1155.79 1157.54 24.63 5.19

Critical Chi-Square Value ( 24,05.0χ ) 9.49 9.49

Table 5.22: Goodness-of-Fit Results of NB & EB Models - Highway Speed

Highway Sped (mph)

Number of Observed

Accidents Used in Developing

Models

Predicted Frequency of Accidents for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

1_20 88 84.48 86.40 0.15 0.03

21_25 269 255.39 262.81 0.73 0.15

26_30 220 180.42 202.00 8.69 1.60

31_45 299 395.66 342.96 23.61 5.63

Over 45 283 239.84 263.37 7.77 1.46

Grand Total 1159 1155.79 1157.54 40.94 8.88

Critical Chi-Square Value ( 24,05.0χ ) 9.49 9.49

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Table 5.23: Goodness-of-Fit Results of NB & EB Models - Number of Traffic Lanes

Number of Traffic Lanes

Number of Observed

Accidents Used in Developing

Models

Predicted Frequency of Accidents for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

1 102 94.05 98.38 0.67 0.13

2 1041 1049.17 1044.71 0.06 0.01

3 3 5.18 3.99 0.92 0.25

4 12 5.62 9.10 7.24 0.92

Over 4 1 1.78 1.35 0.34 0.09

Grand Total 1159 1155.79 1157.54 9.23 1.41

Critical Chi-Square Value ( 24,05.0χ ) 9.49 9.49

Table 5.24: Goodness-of-Fit Results of NB & EB Models - Daily Train Movement

Daily Train Movement

(trains)

Number of Observed

Accidents Used in Developing

Models

Predicted Frequency of Accidents for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

1_2 249 250.74 249.79 0.01 0.00

3_5 166 180.25 172.48 1.13 0.24

6_10 288 289.57 288.71 0.01 0.00

11_20 210 177.48 195.21 5.96 1.12

Over 20 246 257.75 251.34 0.54 0.11

Grand Total 1159 1155.79 1157.54 7.64 1.48

Critical Chi-Square Value ( 24,05.0χ ) 9.49 9.49

Table 5.25: Goodness-of-Fit Results of NB & EB Models - Annual Average Daily Traffic

Annual Average of Daily Traffic (vehicles)

Number of Observed

Accidents Used in Developing

Models

Predicted Frequency of Accidents for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

1_100 291 261.11 277.41 3.42 0.67

101_250 199 251.54 222.89 10.98 2.56

251_500 231 238.58 234.44 0.24 0.05

501_1000 171 147.31 160.23 3.81 0.72

Over 1000 267 257.25 262.56 0.37 0.07

Grand Total 1159 1155.79 1157.54 18.82 4.08

Critical Chi-Square Value ( 24,05.0χ ) 9.49 9.49

Specific Calcula t ions for Acc idents Predi c t ion at Grade Crossings using EB Model

Consider the crossing (ID No: 831207B) with the historical data of three (3)

accidents in the period 2001-2005; maximum timetable train speed (50); highway

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speed (55); number of traffic lanes (2); daily train movement (25) and annual average

daily traffic (839). Using the Equation 5.52, the NB model predicts the number of

accidents at this grade crossing in the five-year period as:

=+++++= (839)]Ln *0.300 (25)Ln * 0.484 2 * 0.31355 * 0.014 50 * 0.015 -5.822[)(ˆ

831207BeYE 0.90

From Table 5.20, the values of weighting factors are: =1ω 0.5453 and =2ω 0.4547. By

the Equation 5.53, the EB model predicts the number of accidents at this grade

crossing in the five-year period as:

=+= 90.0*4547.03*5453.0),(ˆ8831207B

yYE 2.04

In a similar manner, the number of accidents was estimated for crossing in the group

using the NB and EB models and the relevant values were recorded. For example,

Table 5.26 reveals the top ten accidental crossings predicted by the EB model in the

group.

Table 5.26: Top Ten Accidental Locations by EB Model Prediction in Protection Type 2

Grade Crossing

ID

Number of Accidents in

History (5 Years)

Prediction of Accidents Using

NB Model (5 Years)

Prediction of Accidents Using EB

Model (5 Years)

376009B 9 1.03 5.38

870677P 2 3.29 2.59

378243Y 4 0.50 2.41

020046T 4 0.13 2.24

831207B 3 0.90 2.04

639317L 3 0.89 2.04

062818S 3 0.69 1.95

191359D 3 0.69 1.95

727316W 3 0.43 1.83

720776A 3 0.38 1.81

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5.5.1.3 Crossing Protection Type 3 (Signals, Bells or Warning Devices)

In the Protection Type 3, a total of 2,723 accidents were reported during the 2001-

2005 period in the USA. In this group, only 2,130 crossings (5.41%) out of 39,397

crossings experienced accidents. This means that the data contains several zero-

accident occurrences. This tendency presents problems in predicting the accidents at

grade crossings using the simple Poisson model. There are only 4,121 records

considered suitable for model development once the other records, which have data

quality issues with variables, have been discarded. The value of 7 was recorded for

the maximum number of accidents at a given crossing in this group. Descriptive

statistics of eight variables, which were considered to initiate the model development,

are summarised in Table 5.27.

Table 5.27: Descriptive Statistics on Variables Used in the Model - Protection Type 3

Crossing Protection Type 3 Count Minimum Maximum Mean Std. Deviation

Number of Accidents in 5 Years 4121 0 7 0.18 0.51

Daily Train Movement 4121 1 112 9.10 11.25

Annual Average Daily Traffic 4121 20 115844 4069.48 5974.69

Maximum Timetable Train Speed 4121 1 79 30.29 16.18

Highway Speed 4121 5 70 34.03 9.63

Number of Main Tracks 4121 1 5 1.04 0.21

Number of Traffic Lanes 4121 1 9 2.24 0.72

Track Crossing Angle 4121 1 3 2.74 0.51

In the early part of modeling analysis in this group, Pearson correlation values for the

independent variables were estimated and shown in Table 5.28. As these variables

show reasonably low values in correlation, all of them were initially selected in the

process of model development.

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Table 5.28: Pearson Correlation Between Variables Used in the Model - Protection Type 3

Crossing Protection Type 3

Daily Train

Movement

Annual

Average

Daily Traffic

Maximum

Timetable

Train Speed

Highway

Speed

Number of

Main Tracks

Number of

Traffic

Lanes

Track

Crossing

Angle

Daily Train Movement 1.00 -0.17 0.39 -0.15 0.17 -0.12 0.05

Annual Average Daily Traffic -0.17 1.00 -0.27 0.06 -0.04 0.62 -0.06

Maximum Timetable Train

Speed 0.39 -0.27 1.00 -0.04 0.08 -0.23 0.05

Highway Speed -0.15 0.06 -0.04 1.00 -0.08 0.04 -0.13

Number of Main Tracks 0.17 -0.04 0.08 -0.08 1.00 -0.01 0.04

Number of Traffic Lanes -0.12 0.62 -0.23 0.04 -0.01 1.00 -0.03

Track Crossing Angle 0.05 -0.06 0.05 -0.13 0.04 -0.03 1.00

a. GLM Poisson Regression Model

For the Poisson model, seven independent variables were initially investigated. Five

of the seven variables (daily train movement, annual average daily traffic, maximum

timetable train speed, highway speed and number of traffic lanes) were found to be

statistically significant at 5% level (Table 5.29). The discarded variables were

number of main tracks and track crossing angle as their significance values showed

more than 0.05. Table 5.30 shows the goodness-of-fit details on the GLM Poisson

Regression model.

Table 5.29: Parameter Estimates of GLM Poisson Regression Model - Protection Type 3

Parameter B Std. Error

95% Wald Confidence

Interval Hypothesis Test

Lower Upper Wald Chi-Square df Sig.

(Intercept) -5.913 0.327 -6.553 -5.273 327.903 1 0.000

MTTS 0.013 0.002 0.008 0.018 27.092 1 0.000

HS 0.012 0.004 0.004 0.020 9.025 1 0.003

TL 0.240 0.042 0.157 0.323 32.175 1 0.000

Ln (DT) 0.385 0.043 0.301 0.469 80.096 1 0.000

Ln (AADT) 0.273 0.035 0.204 0.342 60.513 1 0.000

(Scale) a

1

Dependent Variable: NTA

Model: (Intercept), MTTS, HS, TL, Ln (DT), Ln (AADT)

a - Fixed at the displayed value.

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Table 5.30: Goodness-of-Fit Detail of GLM Poisson Regression Model - Protection Type 3

Crossing Protection Type 3 Value df Value / df

Deviance 2772.4 4115 0.674

Scaled Deviance 2772.4 4115

Pearson Chi-Square 5029.7 4115 1.222

Scaled Pearson Chi-Square 5029.7 4115

Log Likelihood(a) -2036.9

Akaike's Information Criterion (AIC) 4085.7

Finite Sample Corrected AIC (AICC) 4085.7

Bayesian Information Criterion (BIC) 4123.7

Consistent AIC (CAIC) 4129.7

Dependent Variable: NTA

Model: (Intercept), MTTS, HS, TL, Ln (DT), Ln (AADT)

Accident Predic t ion Equat ion from GLM Model (Poisso n Regression)

According to results obtained from the Poisson model, the expected number of

accidents per 5 years at each crossing is expressed as:

(AADT)]Ln *0.273 (DT)Ln * 0.385 TL * 0.240HS * 0.012 MTTS * 0.013 -5.913[3)(ˆ +++++= eGYE (5.55)

where 3)(ˆ

GYE - Number of accidents expected to occur at a crossing in Group3 in 5

years.

b. GLM Negat ive Binomia l Regression Model

The Negative Binomial model reflects on the same explanatory variables which were

selected for the above-mentioned Poisson model. However, the parameter estimation

values on these variables in the NB model show a slight difference from the Poisson

model (Table 5.31). Table 5.32 shows the goodness-of-fit details on the GLM

Negative Binomial Regression model.

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Table 5.31: Parameter Estimates of GLM Negative Binomial Model - Protection Type 3

Parameter B Std. Error

95% Wald Confidence

Interval Hypothesis Test

Lower Upper Wald Chi-Square df Sig.

(Intercept) -5.750 0.362 -6.460 -5.040 252.020 1 0.000

MTTS 0.013 0.003 0.008 0.019 21.928 1 0.000

HS 0.010 0.004 0.002 0.019 5.549 1 0.018

TL 0.252 0.051 0.153 0.352 24.543 1 0.000

Ln (DT) 0.359 0.049 0.264 0.454 54.573 1 0.000

Ln (AADT) 0.261 0.039 0.184 0.337 44.732 1 0.000

(Scale) a

1

Dependent Variable: NTA

Model: (Intercept), MTTS, HS, TL, Ln (DT), Ln (AADT)

a - Fixed at the displayed value.

Table 5.32: Goodness-of-Fit Results of GLM Negative Binomial Model - Protection Type 3

Crossing Protection Type 3 Value df Value / df

Deviance 2175.9 4115 0.529

Scaled Deviance 2175.9 4115

Pearson Chi-Square 4219.1 4115 1.025

Scaled Pearson Chi-Square 4219.1 4115

Log Likelihood(a) -2002.8

Akaike's Information Criterion (AIC) 4017.5

Finite Sample Corrected AIC (AICC) 4017.6

Bayesian Information Criterion (BIC) 4055.5

Consistent AIC (CAIC) 4061.5

Dependent Variable: NTA

Model: (Intercept), MTTS, HS, TL, Ln (DT), Ln (AADT)

Accident Predic t ion Equat ion from GL M Model (Negat ive Binomia l Regression)

According to results obtained from the NB model, the expected number of accidents

per 5 years at each crossing in this group is expressed as:

(AADT)]Ln *0.261 (DT)Ln * 0.359 TL * 0.252HS * 0.010 MTTS * 0.013 -5.750[3)(ˆ +++++= eGYE (5.56)

where 3)(ˆ

GYE - Number of accidents expected to occur at a crossing in Group3 in 5

years.

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Goodness-of-Fit Results and Comparisons betw een Poiss on and NB Models

By referring the goodness-of-fit values, the Poisson model yielded a Pearson Chi-

Square (value per degrees of freedom) to 1.222 suggesting a minor amount of over-

dispersion in the data (Table 5.30). The Negative Binomial model shows (Table 5.32)

a slightly better result in Pearson Chi-Square value (1.025). In comparison of the

Akaike's Information Criterion (AIC), the value of the NB model (4017.5) is slightly

smaller than that of the Poisson model (4085.7). In addition, the values for mean and

variance of the accident count data for Protection Type 3 crossings show 0.18 and

0.26 respectively. Since the Poisson model requires the mean and variance to be

equal, it is unsuitable for data with greater variance than mean. The Negative

Binomial may be more appropriate in such settings as its variance is always larger

than the mean. Based on these findings, the NB model is therefore considered to be

more appropriate than the Poisson model in the initial process of accidents

prediction. The Empirical Bayesian model is then used with adjustment to the NB

model developed in order to enhance the quality of prediction.

c. Empirica l Bayesian Model (Adjustm ent to GLM NB Regression Model

Results)

In accordance with the equations 5.24, 5.25 and 5.27 the weighting factors (1ω and

2ω ) and the over-dispersion parameter (κ ) for the Protection Type 3 crossings were

calculated and are shown in Table 5.33.

Table 5.33: Over-Dispersion Parameter and Weighting Factors Estimation - EB Model

Crossing Protection Type 3

Mean of Accidents Estimated by NB Model - )(ˆ YE 0.1837

Variance of Accidents - )(YVar 0.2568

Over-Dispersion Parameter - κ 0.1314

Weighting Factor - 1ω 0.5819

Weighting Factor - 2ω 0.4181

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Accident Predic t ion Equat ion from EB Model

The EB model prediction based on the adjustment to the NB model results shows that

the expected number of accidents per 5 years at each crossing in the Protection

Type 3 is expressed as:

3)(ˆ*2*13),(ˆGYEyGyYE ωω += (5.57)

or:

(AADT)]Ln *0.261 (DT)Ln * 0.359 TL * 0.252HS * 0.010 MTTS * 0.013 -5.750[*4181.0*5819.0),(ˆ

3

++++++= eyyYEG (5.58)

where 3),(ˆ

GyYE - Number of accidents (predicted by EB Model) expected to occur at a

crossing in Group3 in 5 years.

Comparison of Goodness-of-Fit Results betw een EB and NB Models for Fina l

Select ion

A Chi-square goodness-of-fit test was separately applied to the test results obtained

by the NB and EB models for each of the explanatory variables. The Chi-square

goodness-of-fit values for maximum timetable train speed, highway speed, number

of traffic lanes, daily train movement and annual average daily traffic are calculated

and shown in Tables 5.34, 5.35, 5.36, 5.37 and 5.38 respectively. For these

explanatory variables the calculated Chi-square values on the NB model showed

5.25, 37.58, 13.40, 27.43 and 5.26 respectively. However, only two of them are

found to be less than the critical value (2

4,05.0χ = 9.49) at the 5% level of significance.

The calculated Chi-square values on the EB model showed 0.89, 6.29, 2.22, 4.81 and

0.92 respectively. All of these values are less than the critical value for the

explanatory variables. In comparison to calculated Chi-square values, the EB model

shows a better result than the NB model in all cases. In addition, the EB model

estimates the R-square (R2) value of 0.38. This means that the model has explained

38% of the original variability, and is left with 62% residual variability. In summary,

even though this group of crossings (with Signals, Bells or Warning Devices)

suggested a minor problem of over-dispersion in the accidents data, the EB model is

more statistically acceptable for prediction of accidents.

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Table 5.34: Goodness-of-Fit Results of NB & EB Models - Max Timetable Train Speed

Maximum Time Table Train Speed

(mph)

Number of Observed

Accidents Used in Developing

Models

Predicted Frequency of Accidents for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

1_20 201 197.39 199.49 0.07 0.01

21_30 199 216.95 206.51 1.49 0.27

31_40 131 113.53 123.70 2.69 0.43

41_50 119 111.41 115.82 0.52 0.09

Over 50 107 114.52 110.14 0.49 0.09

Grand Total 757 753.80 755.66 5.25 0.89

Critical Chi-Square Value ( 24,05.0χ ) 9.49 9.49

Table 5.35: Goodness-of-Fit Results of NB & EB Models - Highway Speed

Highway Sped (mph)

Number of Observed

Accidents Used in Developing

Models

Predicted Frequency of Accidents for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

1_25 195 176.18 187.13 2.01 0.33

26_30 209 213.88 211.04 0.11 0.02

31_35 158 155.19 156.83 0.05 0.01

36_50 101 149.00 121.07 15.46 3.33

Over 50 94 59.54 79.59 19.95 2.61

Grand Total 757 753.80 755.66 37.58 6.29

Critical Chi-Square Value ( 24,05.0χ ) 9.49 9.49

Table 5.36: Goodness-of-Fit Results of NB & EB Models - Number of Traffic Lanes

Number of Traffic Lanes

Number of Observed

Accidents Used in Developing

Models

Predicted Frequency of Accidents for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

1 3 5.41 4.01 1.07 0.25

2 587 580.89 584.44 0.06 0.01

3 34 24.41 29.99 3.76 0.54

4 94 115.34 102.92 3.95 0.77

Over 4 39 27.76 34.30 4.55 0.64

Grand Total 757 753.80 755.66 13.40 2.22

Critical Chi-Square Value ( 24,05.0χ ) 9.49 9.49

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Table 5.37: Goodness-of-Fit Results of NB & EB Models - Daily Train Movement

Daily Train Movement

(trains)

Number of Observed

Accidents Used in Developing

Models

Predicted Frequency of Accidents for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

1_2 174 145.02 161.89 5.79 0.91

3_5 111 145.80 125.55 8.30 1.69

6_10 168 198.60 180.79 4.71 0.91

11_25 169 158.33 164.54 0.72 0.12

Over 25 135 106.05 122.90 7.90 1.19

Grand Total 757 753.80 755.66 27.43 4.81

Critical Chi-Square Value ( 24,05.0χ ) 9.49 9.49

Table 5.38: Goodness-of-Fit Results of NB & EB Models - Annual Average Daily Traffic

Annual Average of Daily Traffic (vehicles)

Number of Observed

Accidents Used in Developing

Models

Predicted Frequency of Accidents for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

1_1000 173 194.26 181.89 2.33 0.43

1001_2500 177 164.64 171.83 0.93 0.16

2501_5000 137 122.04 130.75 1.83 0.30

5001_10000 132 136.51 133.88 0.15 0.03

Over 10000 138 136.35 137.31 0.02 0.00

Grand Total 757 753.80 755.66 5.26 0.92

Critical Chi-Square Value ( 24,05.0χ ) 9.49 9.49

Specific Calcula t ions for Acc idents Predi c t ion at Grade Crossings using EB Model

Consider the crossing (ID No: 303631P) with the historical data of four (4) accidents

in the period of 2001-2005; maximum timetable train speed (49); highway speed

(30); number of traffic lanes (5); daily train movement (4) and annual average daily

traffic (11499). Using the Equation 5.56, the NB model predicts the number of

accidents at this grade crossing in the five-year period as:

=+++++= (11499)]Ln *0.261 (4)Ln * 0.359 5 * 0.25230 * 0.010 49 * 0.013 -5.750[)(ˆ

303631PeYE 0.55

From Table 5.33, the values of weighting factors are: =1ω 0.5819 and =2ω 0.4181. By

the Equation 5.53, the EB model predicts the number of accidents at this grade

crossing in the five-year period as:

=+= 55.0*4181.04*5819.0),(ˆ303631P

yYE 2.56

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Similarly, the number of accidents was estimated for crossing in the group using the

NB and EB models and the relevant values were recorded. For example, Table 5.39

reveals the top ten accidental crossings predicted by EB model in the group.

Table 5.39: Top Ten Accidental Locations by EB Model Prediction in Protection Type 3

Grade Crossing

ID

Number of Accidents in

History (5 Years)

Prediction of Accidents Using

NB Model (5 Years)

Prediction of Accidents Using EB

Model (5 Years)

640124J 7 0.44 4.26

478051H 6 0.82 3.83

879204S 5 1.13 3.38

351319Y 5 0.62 3.17

342474E 5 0.41 3.08

729216Y 5 0.31 3.04

303631P 4 0.55 2.56

351290D 4 0.37 2.48

327023N 4 0.29 2.45

163624R 4 0.10 2.37

5.5.1.4 Crossing Protection Type 4 (Gates or Full Barrier)

A total of 5,442 accidents in the Protection Type 4 were reported during the 2001-

2005 period in the USA. In this group, only 4,297 crossings (10.23%) out of 41,997

crossings experienced accidents. This shows the data are dominant with zero-

accident occurrences. This tendency presents problems in predicting accidents at

grade crossings using the simple Poisson model. There are only 7,942 records

considered suitable for model development once g the other records, which have data

quality issues with variables, have been discarded. The value of 6 was recorded for

the maximum number of accidents at a given crossing in this group. Descriptive

statistics of eight variables, which were considered to initiate the model development,

are summarised in Table 5.40.

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Table 5.40: Descriptive Statistics on Variables Used in the Model - Protection Type 4

Crossing Protection Type 4 Count Minimum Maximum Mean Std. Deviation

Number of Accidents in 5 Years 7942 0 6 0.19 0.51

Daily Train Movement 7942 1 255 24.24 23.43

Annual Average Daily Traffic 7942 1 308661 4255.65 7822.78

Maximum Timetable Train Speed 7942 5 110 49.59 18.14

Highway Speed 7942 5 70 35.39 10.93

Number of Main Tracks 7942 0 7 1.28 0.50

Number of Traffic Lanes 7942 1 9 2.26 0.76

Track Crossing Angle 7942 1 3 2.81 0.44

In the early part of modeling analysis in this group, Pearson correlation values for the

independent variables were estimated and shown in Table 5.41. As these variables

show reasonably low values in correlation, all of them were initially selected in the

process of model development.

Table 5.41: Pearson Correlation Between Variables Used in the Model - Protection Type 4

Crossing Protection Type 4

Daily Train

Movement

Annual

Average

Daily Traffic

Maximum

Timetable

Train Speed

Highway

Speed

Number of

Main Tracks

Number of

Traffic

Lanes

Track

Crossing

Angle

Daily Train Movement 1.00 0.07 0.40 -0.09 0.58 0.08 0.05

Annual Average Daily Traffic 0.07 1.00 -0.08 -0.02 0.10 0.49 -0.04

Maximum Timetable Train

Speed 0.40 -0.08 1.00 0.07 0.27 -0.11 0.05

Highway Speed -0.09 -0.02 0.07 1.00 -0.08 -0.01 -0.11

Number of Main Tracks 0.58 0.10 0.27 -0.08 1.00 0.10 0.02

Number of Traffic Lanes 0.08 0.49 -0.11 -0.01 0.10 1.00 -0.04

Track Crossing Angle 0.05 -0.04 0.05 -0.11 0.02 -0.04 1.00

a. GLM Poisson Regression Model

For the Poisson model, seven independent variables were initially investigated. Four

of the seven variables (daily train movement, annual average daily traffic, number of

main tracks and number of traffic lanes) were found to be statistically significant at

5% level (Table 5.42). The discarded variables were maximum timetable train speed,

highway speed and track crossing angle as their significance values showed more

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than 0.05. Table 5.43 shows the goodness-of-fit details on the GLM Poisson

Regression model.

Table 5.42: Parameter Estimates of GLM Poisson Regression Model - Protection Type 4

Parameter B Std. Error

95% Wald Confidence

Interval Hypothesis Test

Lower Upper Wald Chi-Square df Sig.

(Intercept) -4.399 0.164 -4.720 -4.079 723.668 1 0.000

MT 0.187 0.053 0.084 0.290 12.704 1 0.000

TL 0.150 0.029 0.092 0.207 26.083 1 0.000

Ln (DT) 0.243 0.032 0.182 0.305 59.633 1 0.000

Ln (AADT) 0.182 0.021 0.140 0.224 71.942 1 0.000

(Scale) a

1

Dependent Variable: NTA

Model: (Intercept), MT, TL, Ln (DT), Ln (AADT)

a - Fixed at the displayed value.

Table 5.43: Goodness-of-Fit Detail of GLM Poisson Regression Model - Protection Type 4

Crossing Protection Type 4 Value df Value / df

Deviance 5574.5 7937 0.702

Scaled Deviance 5574.5 7937

Pearson Chi-Square 10585.8 7937 1.334

Scaled Pearson Chi-Square 10585.8 7937

Log Likelihood(a) -4031.5

Akaike's Information Criterion (AIC) 8073.0

Finite Sample Corrected AIC (AICC) 8073.0

Bayesian Information Criterion (BIC) 8107.9

Consistent AIC (CAIC) 8112.9

Dependent Variable: NTA

Model: (Intercept), MT, TL, Ln (DT), Ln (AADT)

Accident Predic t ion Equat ion from GLM Model (Poisso n Regression)

According to results obtained from the Poisson model, the expected number of

accidents per 5 years at each crossing is expressed as:

(AADT)]Ln *0.182 (DT)Ln * 0.243 TL * 0.150 MT * 0.187 -4.399[4)(ˆ ++++= eGYE (5.59)

where 4)(ˆ

GYE - Number of accidents expected to occur at a crossing in Group4 in 5

years.

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b. GLM Negat ive Binomia l Regression Model

The Negative Binomial model reflects on the same explanatory variables, which

were selected for the above-mentioned Poisson model. However, the parameter

estimation values on these variables in the NB model show a slight difference from

the Poisson model (Table 5.44). Table 5.45 shows the goodness-of-fit details on the

GLM Negative Binomial Regression model.

Table 5.44: Parameter Estimates of GLM Negative Binomial Model - Protection Type 4

Parameter B Std. Error

95% Wald Confidence

Interval Hypothesis Test

Lower Upper Wald Chi-Square df Sig.

(Intercept) -4.383 0.181 -4.738 -4.028 586.397 1 0.000

MT 0.185 0.060 0.067 0.303 9.493 1 0.002

TL 0.167 0.034 0.100 0.235 23.773 1 0.000

Ln (DT) 0.248 0.035 0.180 0.317 50.608 1 0.000

Ln (AADT) 0.173 0.024 0.127 0.219 54.014 1 0.000

(Scale) a

1

Dependent Variable: NTA

Model: (Intercept), MT, TL, Ln (DT), Ln (AADT)

a - Fixed at the displayed value.

Table 5.45: Goodness-of-Fit Results of GLM Negative Binomial Model - Protection Type 4

Crossing Protection Type 4 Value df Value / df

Deviance 4357.1 7937 0.549

Scaled Deviance 4357.1 7937

Pearson Chi-Square 8960.3 7937 1.129

Scaled Pearson Chi-Square 8960.3 7937

Log Likelihood(a) -3931.2

Akaike's Information Criterion (AIC) 7872.4

Finite Sample Corrected AIC (AICC) 7872.4

Bayesian Information Criterion (BIC) 7907.3

Consistent AIC (CAIC) 7912.3

Dependent Variable: NTA

Model: (Intercept), MT, TL, Ln (DT), Ln (AADT)

Accident Predic t ion Equat ion from GL M Model (Negat ive Binomia l Regression)

According to results obtained from the NB model, the expected number of accidents

per 5 years at each crossing in this group is expressed as:

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(AADT)]Ln *0.173 (DT)Ln * 0.248 TL * 0.167 MT * 0.185 -4.383[4)(ˆ ++++= eGYE (5.60)

where: 4)(ˆ

GYE - Number of accidents expected to occur at a crossing in Group4 in 5

years.

Goodness-of-Fit Results and Comparisons betw een Poiss on and NB Models

By referring the goodness-of-fit values, the Poisson model yielded a Pearson Chi-

Square (value per degrees of freedom) to 1.334 suggesting a minor amount of over-

dispersion in the data (Table 5.43). The Negative Binomial model (Table 5.45) shows

a slightly better result in Pearson Chi-Square value (1.129). In comparison with the

Akaike's Information Criterion (AIC), the value of the NB model (7872.4) is smaller

than that of the Poisson model (8073.0). In addition, the values for mean and

variance of the accident count data for Protection Type 4 crossings show 0.19 and

0.26 respectively. Since the Poisson model requires the mean and variance to be

equal, it is unsuitable for data with greater variance than mean. The Negative

Binomial may be more appropriate in such settings as its variance is always larger

than the mean. Based on these findings, the NB model is therefore considered to be

more appropriate than the Poisson model in the initial process of accidents

prediction. The Empirical Bayesian model is then used with adjustment to the NB

model developed in order to enhance the quality of prediction.

c. Empirica l Bayesian Model (Adjustm ent to GLM NB Regression Model

Results)

In accordance with the above-mentioned equations 5.24, 5.25 and 5.27, the weighting

factors ( 1ω and 2ω ) and the over-dispersion parameter (κ ) for the Protection Type 4

crossings were calculated and are shown in Table 5.46.

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Table 5.46: Over-Dispersion Parameter and Weighting Factors Estimation - EB Model

Crossing Protection Type 4

Mean of Accidents Estimated by NB Model - )(ˆ YE 0.1851

Variance of Accidents - )(YVar 0.2624

Over-Dispersion Parameter - κ 0.1305

Weighting Factor - 1ω 0.5864

Weighting Factor - 2ω 0.4136

Accident Predic t ion Equat ion from EB Model

The EB model prediction based on the adjustment to the NB model results shows that

the expected number of accidents per 5 years at each crossing in the Protection

Type 4 is expressed as:

4)(ˆ*2*14),(ˆGYEyGyYE ωω += (5.61)

or:

(AADT)]Ln *0.173 (DT)Ln * 0.248 TL * 0.167 MT * 0.185 -4.383[*4136.0*5864.0),(ˆ

4

+++++= eyyYEG (5.62)

where 4),(ˆ

GyYE - Number of accidents (predicted by EB Model) expected to occur at a

crossing in Group4 in 5 years.

Comparison of Goodness-of-Fit Results betw een EB and NB Models for Fina l

Select ion

A Chi-square goodness-of-fit test was separately applied to the test results obtained

by the NB and EB models for each of the explanatory variables. The Chi-square

goodness-of-fit values for number of main tracks, number of traffic lanes, daily train

movement and annual average daily traffic are calculated and shown in Tables 5.47,

5.48, 5.49 and 5.50 respectively. For these explanatory variables the calculated Chi-

square values on the NB model showed 179.25, 23.69, 9.41 and 8.93 respectively.

However, only two of them are found to be less than the critical value (2

4,05.0χ = 9.49)

at the 5% level of significance. The calculated Chi-square values on the EB model

showed 5.13, 2.18, 1.59 and 1.52 respectively. All of these values are less than the

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critical value for the explanatory variables. In comparison to calculated Chi-square

values, the EB model shows better result than the NB model in all cases. In addition,

the EB model estimates the R-square (R2) value of 0.44. This means that the model

has explained 44% of the original variability, and is left with 56% residual

variability. In summary, even though this group of crossings (with Gates or Full

Barrier) suggested a minor problem of over-dispersion in the accidents data, the EB

model is more statistically acceptable for prediction of accidents.

Table 5.47: Goodness-of-Fit Results of NB & EB Models - Number of Main Tracks

Number of Main Tracks

Number of Observed

Accidents Used in Developing

Models

Predicted Frequency of Accidents for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

0 21 2.04 13.16 175.95 4.67

1 869 893.07 878.95 0.65 0.11

2 511 514.45 512.43 0.02 0.00

3 60 54.96 57.92 0.46 0.07

Over 3 9 5.54 7.57 2.17 0.27

Grand Total 1470 1470.05 1470.02 179.25 5.13

Critical Chi-Square Value ( 24,05.0χ ) 9.49 9.49

Table 5.48: Goodness-of-Fit Results of NB & EB Models - Number of Traffic Lanes

Number of Traffic Lanes

Number of Observed

Accidents Used in Developing

Models

Predicted Frequency of Accidents for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

1 21 7.88 15.57 21.86 1.89

2 1086 1107.78 1095.01 0.43 0.07

3 49 41.37 45.85 1.41 0.22

4 244 243.34 243.73 0.00 0.00

Over 4 70 69.68 69.87 0.00 0.00

Grand Total 1470 1470.05 1470.02 23.69 2.18

Critical Chi-Square Value ( 24,05.0χ ) 9.49 9.49

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Table 5.49: Goodness-of-Fit Results of NB & EB Models - Daily Train Movement

Daily Train Movement

(trains)

Number of Observed

Accidents Used in Developing

Models

Predicted Frequency of Accidents for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

1_8 262 288.13 272.81 2.37 0.43

9_20 308 333.62 318.60 1.97 0.35

21_30 288 255.61 274.61 4.10 0.65

31_50 320 316.81 318.68 0.03 0.01

Over 50 292 275.88 285.33 0.94 0.16

Grand Total 1470 1470.05 1470.02 9.41 1.59

Critical Chi-Square Value ( 24,05.0χ ) 9.49 9.49

Table 5.50: Goodness-of-Fit Results of NB & EB Models - Annual Average Daily Traffic

Annual Average of Daily Traffic (vehicles)

Number of Observed

Accidents Used in Developing

Models

Predicted Frequency of Accidents for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

1_500 234 224.23 229.96 0.43 0.07

501_2000 329 357.39 340.74 2.25 0.40

2001_5000 271 295.54 281.15 2.04 0.37

5001_10000 283 275.61 279.95 0.20 0.03

Over 10000 353 317.29 338.23 4.02 0.64

Grand Total 1470 1470.05 1470.02 8.93 1.52

Critical Chi-Square Value ( 24,05.0χ ) 9.49 9.49

Specific Calcula t ions for Acc idents Predi c t ion at Grade Crossings using EB Model

Consider the crossing (ID No: 372131E) with the historical data of four (4) accidents

in the period of 2001-2005; number of main tracks (3); number of traffic lanes (4);

daily train movement (106) and annual average daily traffic (25084). Using the

Equation 5.60, the NB model predicts the number of accidents at this grade crossing

in the five-year period as:

=++++= (25084)]Ln *0.173 (106)Ln * 0.248 4 * 0.167 3 * 0.185 -4.383[)(ˆ

372131EeYE 0.78

From Table 5.46, the values of weighting factors are: =1ω 0.5864 and =2ω 0.4136. By

the Equation 5.61, the EB model predicts the number of accidents at this grade

crossing in the five-year period as:

=+= 78.0*4136.04*5864.0),(ˆ372131E

yYE 2.67

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Similarly, the number of accidents was estimated for crossing in the group using the

NB and EB models and the relevant values were recorded. For example, Table 5.51

reveals the top ten accidental crossings predicted by the EB model in the group.

Table 5.51: Top Ten Accidental Locations by EB Model Prediction in Protection Type 4

Grade Crossing

ID

Number of Accidents in

History (5 Years)

Prediction of Accidents Using

NB Model (5 Years)

Prediction of Accidents Using EB

Model (5 Years)

732161S 6 0.55 3.75

326963Y 6 0.32 3.65

720880U 6 0.32 3.65

155613H 6 0.22 3.61

140730J 5 0.27 3.04

726588F 5 0.26 3.04

522646H 5 0.26 3.04

607213R 5 0.14 2.99

372131E 4 0.78 2.67

522506F 4 0.58 2.59

5.5.2 Generating Models Predic ting Accidental Consequences

As indicated earlier, limited research has been carried out in the past on developing

models for predicting railway-highway grade crossing accident consequences.

Another major part of this work has been to establish a statistical relationship

between predicted consequences and various characteristic factors or attributes at the

railway-highway grade crossings. In particular, factors including fatalities, personal

injuries, and property and vehicle damage are considered as the main accident

severity consequences. Since these consequences contribute disproportionately to

accident severity, each of them had to be weighted according to their reported costs

in the past. These costs will form a uniform value or yardstick by which different

statuses of accidental consequences can be compared. The weighted sum of all

accidental consequences yields a score known as ‘Equivalent Fatality Score’.

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Formulae Generat ing ‘Equiva lent Fata lity Score ’

According to research by Canada's Waterloo University (2003), these weights

assigned to fatalities and personal injuries were based on 1995 United States National

Safety Council cost estimates from California Life-cycle Benefit/Cost Analysis

Model (California Department of Transportation 1999). For property and vehicle

damage, weights were obtained from estimates provided by the US Federal Railroad

Administration using a willingness-to-pay approach. The average cost of different

accident consequences were reported by the FRA in US$ (1995) as:

• $2,710,000 for a fatality;

• $65,590 for an injury; and

• $61,950 per train accident for property damage.

The weight for fatality is set equal to ‘1’ (as shown in Table 5.52) and scaled

accordingly for other consequences to yield the ‘Equivalent Fatality Score’ in the

form of equation as:

PVD/61950)*(0.0229+INJ*0.0243+FAT*1 = EFS (5.63)

where:

EFS - Equivalent Fatality Score;

FAT - Number of fatalities;

INJ - Number of Injuries; and

PVD - Property and vehicle damage in dollars.

Table 5.52: Equivalent Fatality Score Comparison for Various Accident Consequences

Jurisdiction Fatality Injury Property / Vehicle Damage

Average Cost in US$

(Saccomanno, 1995) $2,710,000 $65,950 $61,950

Equivalent Fatality Score 1.0000 0.0243 0.0229

The “Equivalent Fatality Score” reflects the severity of accidents at grade crossings

based on the number of fatalities, injuries, and property and vehicle damage, and is

expressed in a single term of equivalent fatalities. For example, in the past five years,

if a given grade crossing had experienced two accidents which resulted in two

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fatalities, 50 injuries and $3 million worth of property and vehicle damage, the total

Equivalent Fatality Score is estimated as:

EFS = 1*2+0.0243*50+(0.0229*3000000/61950) = 4.33 equivalent fatalities

In other words, this consequence score was developed based on average costs

associated with different levels of accident severity. By using a single consequence

score, the full spectrum of consequences associated with each accident was

represented and incorporated into the black-spots identification process, which is

discussed later. The Equivalent Fatality Score (with nearest non-negative integer

value such as 0,1,2..) is used as the dependent variable in consequences models

development. This consequence score can be related statistically to a number of

crossing characteristics, control factors and measures of exposure, to yield an

estimate of expected consequences or severity at each crossing. Models (predicting

total consequences in terms of equivalent fatalities in a period of five years) were

individually developed for each of the four different protection types of grade

crossings. This means that these models consist of four distinctive expressions and

treat the protection types separately. As discussed in the Section 4.1.2.2 of Chapter 4,

only six independent variables are used at the stage of model development for

accidental consequences prediction. All steps involved in the filtering process of

identifying appropriate variables (from the USDOT accident database) prior to

developing a final risk assessment model using statistical methods, were earlier

shown in Table 4.3. Following are the six selected independent variables used in the

consequence models and their abbreviations:

• Maximum Timetable Train Speed (MTTS)

• Highway Speed (HS)

• Number of Main Tracks (MT)

• Number of Traffic Lanes (TL)

• Track Crossing Angle (TCA)

• Total Occupants in Vehicle (TOV)

Using a similar way of predicting best-fit accident frequency models as indicated

earlier, the methods and procedures were used to develop consequence models for

grade crossings in the USA. The procedure was initialised by developing a Poisson

model and was completed by building a Negative Binomial model. The Pearson

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correlation between each variable was checked for existence of high values. The t-

ratios of the parameter estimates of both models were also tested for significance

level at 5%. A drop in the scaled deviance at the 95 % confidence level was also

checked for significance when adding each variable to the model. Both models were

finally tested on values of 2χPearson that are significant at the 95% confidence level

indicating that the models have an acceptable fit to the data. Unlike the accidents

frequency model, few selected variables were found to be statistically significant in

explaining the accidents consequence (severity) model. Maximum train speed and

total occupants in vehicles were found to have a significant effect on the expected

accidents severity at crossings. The consequence prediction model assumes a prior

occurrence of an accident.

5.5.2.1 Crossing Protection Type 1 (No Signs or No signals)

In the Protection Type 1 group of crossings, only five accidents resulted in

consequences with at least one equivalent fatality score during the 2001-2005 period

in the USA. Using the equation of ‘Equivalent Fatality Score’ (Equation 5.63), a total

of six equivalent fatalities were estimated in this group. There were only 91 records

considered suitable for model development once records which have data quality

issues with variables were discarded. The value of 2 was recorded for the maximum

number of Equivalent Fatalities at a given crossing in this group. Descriptive

statistics of seven variables, which were considered to initiate the model

development, are summarised in Table 5.53.

Table 5.53: Descriptive Statistics on Variables Used in the Model - Protection Type 1

Crossing Protection Type 1 Count Minimum Maximum Mean Std. Deviation

Equivalent Fatalities 91 0 2 0.07 0.29

Maximum Timetable Train Speed 91 1 79 23.47 17.38

Highway Speed 91 1 50 9.62 11.87

Number of Main Tracks 91 0 2 0.76 0.64

Number of Traffic Lanes 91 1 4 1.97 0.55

Track Crossing Angle 91 1 3 2.84 0.47

Total Occupants in Vehicle 91 0 5 1.26 0.89

 

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In the early part of modeling analysis in this group, Pearson correlation values for the

independent variables were estimated and shown in Table 5.54. As these variables

show reasonably low values in correlation, all of them were initially selected in the

process of model development.

Table 5.54: Pearson Correlation Between Variables Used in the Model - Protection Type 1

Crossing Protection

Type 1

Maximum Timetable Train

Speed

Highway Speed

Number of Main Tracks

Number of Traffic Lanes

Track Crossing

Angle

Total Occupants in

Vehicle

Maximum Timetable

Train Speed 1.00 -0.27 0.46 -0.18 0.20 0.14

Highway Speed -0.27 1.00 -0.24 0.15 0.09 0.01

Number of Main Tracks 0.46 -0.24 1.00 -0.09 0.28 -0.12

Number of Traffic Lanes -0.18 0.15 -0.09 1.00 -0.02 0.00

Track Crossing Angle 0.20 0.09 0.28 -0.02 1.00 0.02

Total Occupants in

Vehicle 0.14 0.01 -0.12 0.00 0.02 1.00

a. GLM Poisson Regression Model

For the Poisson model, six independent variables were initially investigated. Two of

the six variables (maximum timetable train speed and total occupants in vehicle)

were found to be statistically significant at 5% level (Table 5.55). The discarded

variables were highway speed, number of main tracks, number of traffic lanes and

track crossing angle as their significance values showed more than 0.05. Table 5.56

shows the goodness-of fit-details on the GLM Poisson Regression model.

Table 5.55: Parameter Estimates of GLM Poisson Regression Model for Protection Type 1

Parameter B Std. Error

95% Wald Confidence

Interval Hypothesis Test

Lower Upper Wald Chi-Square df Sig.

(Intercept) -5.586 1.288 -8.109 -3.062 18.821 1 0.000

TOV 0.810 0.378 0.068 1.551 4.575 1 0.032

MTTS 0.043 0.020 0.004 0.082 4.572 1 0.033

(Scale) a

1

Dependent Variable: EFS

Model: (Intercept), TOV, MTTS

a - Fixed at the displayed value

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Table 5.56: Goodness-of-Fit Detail of GLM Poisson Regression Model - Protection Type 1

Crossing Protection Type 1 Value df Value / df

Deviance 19.3 88 0.220

Scaled Deviance 19.3 88

Pearson Chi-Square 49.9 88 0.567

Scaled Pearson Chi-Square 49.9 88

Log Likelihood(a) -17.1

Akaike's Information Criterion (AIC) 40.2

Finite Sample Corrected AIC (AICC) 40.5

Bayesian Information Criterion (BIC) 47.8

Consistent AIC (CAIC) 50.8

Dependent Variable: EFS

Model: (Intercept), TOV, MTTS

Consequences Predic t ion Equat ion of GLM Model (Poisson Regression)

According to the Poisson model, the expected consequences (Equivalent Fatalities)

per accident for 5 years at each crossing are expressed in the form of:

] MTTS*0.043TOV * 0.810 -5.586[1)|(ˆ

++= eGYCE (5.64)

where 1)|(ˆ

GYCE - Number of Equivalent Fatalities expected to sustain at a crossing in

Group1 per 5 years.

b. GLM Negat ive Binomia l Regression Model

The Negative Binomial model reflects on the same variables which were selected for

the above-mentioned Poisson model. However, the parameter estimation values on

these variables in the NB model show considerable changes from the Poisson model

(Table 5.57). Table 5.58 shows the goodness-of-fit details on the GLM Negative

Binomial Regression model.

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Table 5.57: Parameter Estimates of GLM Negative Binomial Model - Protection Type 1

Parameter B Std. Error

95% Wald Confidence

Interval Hypothesis Test

Lower Upper Wald Chi-Square df Sig.

(Intercept) -5.692 1.187 -8.018 -3.366 22.997 1 0.000

TOV 0.789 0.347 0.108 1.470 5.159 1 0.023

MTTS 0.046 0.017 0.014 0.079 7.904 1 0.005

(Scale) a

1

Dependent Variable: EFS

Model: (Intercept), TOV, MTTS

a - Fixed at the displayed value.

Table 5.58: Goodness-of-Fit Results of GLM Negative Binomial Model - Protection Type 1

Crossing Protection Type 1 Value df Value / df

Deviance 22.7 88 0.258

Scaled Deviance 22.7 88

Pearson Chi-Square 55.9 88 0.635

Scaled Pearson Chi-Square 55.9 88

Log Likelihood(a) -16.7

Akaike's Information Criterion (AIC) 39.3

Finite Sample Corrected AIC (AICC) 39.6

Bayesian Information Criterion (BIC) 46.8

Consistent AIC (CAIC) 49.8

Dependent Variable: EFS

Model: (Intercept), TOV, MTTS

Consequences Predic t ion Equat ion of GLM Model (Nega t ive Binomia l Regression)

According to the NB model, the expected consequences (Equivalent Fatalities) per

accident for 5 years at each crossing are expressed in the form of:

] MTTS*0.046TOV * 0.789 -5.692[1)|(ˆ

++= eGYCE (5.65)

where 1

)|(ˆG

YCE - Number of Equivalent Fatalities expected to sustain at a crossing in

Group1 per 5 years.

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Goodness-of-Fit Results and Comparisons betw een Poiss on and NB Models

By referring the goodness-of-fit values, the Poisson model yielded a Pearson Chi-

Square (value per degrees of freedom) to 0.567 suggesting a minor amount of under-

dispersion in the data (Table 5.56). The Negative Binomial model (Table 5.58) shows

a slightly better result in Pearson Chi-Square value (0.635). In comparison of the

Akaike's Information Criterion (AIC), the value of the NB model (39.3) is slightly

smaller than that of the Poisson model (40.2). In addition, the values for mean and

variance of the accidental consequences data for Protection Type 1 crossings show

0.07 and 0.08 respectively. Since the Poisson model requires the mean and variance

to be equal, it is unsuitable for data with greater variance than mean. The Negative

Binomial may be more appropriate in such settings as its variance is always larger

than the mean. Based on these findings, the NB model is therefore considered to be

more appropriate than the Poisson model in the initial process of consequences

prediction. The Empirical Bayesian model is then used with adjustment to the NB

model developed in order to enhance the quality of prediction.

c. Empirica l Bayesian Model (Adjustm ent to GLM NB Regression Model

Results)

Over-dispersion Parameter

Table 5.59: Over-Dispersion Parameter and Weighting Factors Estimation - EB Model

Crossing Protection Type 1

Mean of Consequences Estimated by NB Model - )(ˆ CE 0.0659

Variance of Consequences - )(CVar 0.0845

Over-Dispersion Parameter - κ 0.0134

Weighting Factor - 1ω 0.7154

Weighting Factor - 2ω 0.2846

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Consequences Predic t ion E quat ion of EB Model

1)|(ˆ*21)|(*11)]|(),|[(ˆGYCEGyCGyCYCE ωω +=

(5.66)

or:

] MTTS*0.046TOV * 0.789 -5.692[*2846.01)|(*7154.01)]|(),|[(ˆ

+++= eGyCGyCYCE (5.67)

where 1)|(

GyC - Number of Equivalent Fatalities sustained at a crossing in Group1 in

the five-year history;

1)|(ˆ

GYCE - Number of Equivalent Fatalities (predicted by NB Model) expected to

sustain at a crossing in Group1 per 5 years; and

1)]|(),|[(ˆ

GyCYCE - Number of Equivalent Fatalities (predicted by EB Model which is

adjusted to the NB Model result) expected to sustain at a crossing in Group1 per 5

years.

Comparison of Goodness-of-Fit Results betw een EB and NB Models for Fina l

Select ion

A Chi-square goodness-of-fit test was separately applied to the test results obtained

by the NB and EB models for each of the explanatory variables. The Chi-square

goodness-of-fit values for maximum timetable train speed and total occupants in

vehicle are calculated and shown in Tables 5.60 and 5.61 respectively. For these

explanatory variables the calculated Chi-square values on the NB model showed 1.86

and 7.39 respectively. The values on the EB model showed 0.69 and 1.67

respectively. These results show that both models have Chi-square values less than

the critical value (2

3,05.0χ = 7.82) at 5% level of significance. However, in comparison

to calculated Chi-square values, the EB model shows a better result than the NB

model in all cases. In addition, the EB model estimates the R-square (R2) value of

0.55. This means that the model has explained 55% of the original variability, and is

left with 45% residual variability. In summary, even though this group of crossings

(with No Signs or No Signals) suggested a minor problem of under-dispersion in the

consequences data, the EB model is more statistically acceptable for prediction of

consequences.

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Table 5.60: Goodness-of-Fit Results of NB & EB Models - Max Timetable Train Speed

Maximum Time Table Train Speed

(mph)

Number of Observed Equivalent

Fatalities Used in Developing

Models

Predicted Number of Equivalent Fatalities for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

1 _ 40 4 2.90 3.52 0.42 0.07

41 _ 50 0 0.70 0.31 0.70 0.31

51 _ 60 0 0.69 0.30 0.69 0.30

Over 60 2 1.70 1.87 0.05 0.01

Grand Total 6 6.00 6.00 1.86 0.69

Critical Chi-Square Value ( 23,05.0χ ) 7.82 7.82

Table 5.61: Goodness-of-Fit Results of NB & EB Models - Total Occupants in Vehicle

Total Occupants in

Vehicle

Number of Observed Equivalent

Fatalities Used in Developing

Models

Predicted Number of Equivalent Fatalities for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

0 or 1 0 1.82 0.80 1.82 0.80

2 4 1.44 2.88 4.55 0.44

3 2 1.76 1.89 0.03 0.01

4 or More 0 0.98 0.43 0.98 0.43

Grand Total 6 6.00 6.00 7.39 1.67

Critical Chi-Square Value ( 23,05.0χ ) 7.82 7.82

Specific Calcula t ions for Consequences Pr edic t ion at Grade Crossings using EB

Model

The EB model was originally generated with the actual number of persons occupied

in vehicles at the time of accident. However, the explanatory variable of ‘total

occupants in vehicle’ is an arbitrary value and not a characteristic of a crossing. In

order to identify the worst location, consequences are basically estimated on the

value of one for ‘total occupants in vehicle’ (i.e. one person occupied in a vehicle at

the time of accident) in order to maintain consistency in predicting consequences for

all grade crossings. This technique is applied for all types of protection in the

following analyses.

Consider the crossing (ID No: 632469J) with the historical data of two (2) equivalent

fatalities per accident during the period of 2001-2005; maximum timetable train

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speed (79) and total occupants in vehicle (1); Using the Equation 5.65, the NB model

predicts the total consequences at this grade crossing in the five-year period as:

] 79*0.0461 * 0.789 -5.692[)|(ˆ

632469J

++= eYCE = 0.29

where  

632469J)|(ˆ YCE is the predicted number of equivalent fatalities by NB Model at the

crossing (ID No: 632469J) in the five-year period.

From Table 5.59, the values of weighting factors are: =1ω 0.7154 and =2ω 0.2846.

By the Equation 5.66, the EB model predicts the total consequences at this grade

crossing in the five-year period as:

=+= 29.0*2846.02*7154.0),(ˆ632469J

yYE 1.51

where  

632469J),(ˆ yYE is the refined estimation of equivalent fatalities by EB model at the

crossing (ID No: 632469J) in the five-year period. Similarly, the total consequences were estimated for crossing in the group using the

NB and EB models and the relevant values were recorded. For example, Table 5.62

reveals the top ten locations by consequences predicted with the EB model in the

group.

Table 5.62: Top Ten Locations by Consequence Predicted with EB Model in Protection

Type 1

Grade Crossing

ID

Equivalent Fatalities per

Accident in 5 Years

History

Prediction of Equivalent

Fatalities per Accident Using

NB Model (5 Years)

Prediction of Equivalent Fatalities

per Accident Using EB Model

(5 Years)

632469J 2 0.29 1.51

671860W 1 0.05 0.73

361331H 1 0.03 0.72

022694S 1 0.03 0.72

871032J 1 0.02 0.72

717650P 0 0.29 0.08

723632F 0 0.12 0.03

073290L 0 0.12 0.03

329909R 0 0.10 0.03

731580L 0 0.10 0.03

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5.5.2.2 Crossing Protection Type 2 (Stop Signs or Cross-bucks)

In the Protection Type 2 group of crossings, only 420 accidents resulted in

consequences with at least one equivalent fatality score during the 2001-2005 period

in the USA. Using the equation of ‘Equivalent Fatality Score’, a total of

504 equivalent fatalities were estimated in this group. Followed by discarding the

records, which have data quality issues with variables, only 4,743 records are

considered for the model development. The value of 5 was recorded for the

maximum number of Equivalent Fatalities at a given crossing in this group.

Descriptive statistics of seven variables, which were considered to initiate the model

development, are summarised in Table 5.63.

Table 5.63: Descriptive Statistics on Variables Used in the Model - Protection Type 2

Crossing Protection Type 2 Count Minimum Maximum Mean Std. Deviation

Equivalent Fatalities 4743 0 5 0.11 0.38

Maximum Timetable Train Speed 4743 5 90 40.13 20.11

Highway Speed 4743 1 100 12.23 14.12

Number of Main Tracks 4743 0 3 0.99 0.40

Number of Traffic Lanes 4743 1 6 1.88 0.49

Track Crossing Angle 4743 1 3 2.81 0.45

Total Occupants in Vehicle 4743 0 12 1.24 0.83

 

In the early part of modeling analysis in this group, Pearson correlation values for the

independent variables were estimated and shown in Table 5.64. As these variables

show reasonably low values in correlation, all of them were initially selected in the

process of model development.

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Table 5.64: Pearson Correlation Between Variables Used in the Model - Protection Type 2

Crossing Protection

Type 2

Maximum Timetable Train

Speed

Highway Speed

Number of Main Tracks

Number of Traffic Lanes

Track Crossing

Angle

Total Occupants in

Vehicle

Maximum Timetable

Train Speed 1.00 -0.15 0.44 -0.32 0.07 -0.04

Highway Speed -0.15 1.00 -0.12 0.14 -0.06 0.07

Number of Main Tracks 0.44 -0.12 1.00 -0.24 0.08 -0.02

Number of Traffic Lanes -0.32 0.14 -0.24 1.00 -0.05 0.05

Track Crossing Angle 0.07 -0.06 0.08 -0.05 1.00 -0.03

Total Occupants in

Vehicle -0.04 0.07 -0.02 0.05 -0.03 1.00

a . GLM Poisson Regression Model

For the Poisson model, six independent variables were initially investigated. Two of

the six variables (maximum timetable train speed and total occupants in vehicle)

were found to be statistically significant at 5% level (Table 5.65). The discarded

variables were highway speed, number of main tracks, number of traffic lanes and

track crossing angle as their significance values showed more than 0.05. Table 5.66

shows the goodness-of-fit details on the GLM Poisson Regression model.

Table 5.65: Parameter Estimates of GLM Poisson Regression Model - Protection Type 2

Parameter B Std. Error

95% Wald Confidence

Interval Hypothesis Test

Lower Upper Wald Chi-Square df Sig.

(Intercept) -4.685 0.154 -4.987 -4.383 923.351 1 0.000

TOV 0.411 0.029 0.354 0.467 204.206 1 0.000

MTTS 0.039 0.002 0.034 0.044 259.948 1 0.000

(Scale) a

1

Dependent Variable: EFS

Model: (Intercept), TOV, MTTS

a - Fixed at the displayed value

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Table 5.66: Goodness-of-Fit Detail of GLM Poisson Regression Model - Protection Type 2

Crossing Protection Type 2 Value df Value / df

Deviance 2138.4 4740 0.451

Scaled Deviance 2138.4 4740

Pearson Chi-Square 4776.5 4740 1.008

Scaled Pearson Chi-Square 4776.5 4740

Log Likelihood(a) -1511.4

Akaike's Information Criterion (AIC) 3028.8

Finite Sample Corrected AIC (AICC) 3028.8

Bayesian Information Criterion (BIC) 3048.2

Consistent AIC (CAIC) 3051.2

Dependent Variable: EFS

Model: (Intercept), TOV, MTTS

Consequences Predic t ion Equat ion of GLM Model (Poisson Regression)

The ‘B’ estimate values obtained from the Table 5.65 for the parameters Intercept,

TOV and MTTS are -4.685, 0.411 and 0.039 respectively. According to the Poisson

model, the expected consequences (Equivalent Fatalities) per accident for 5 years at

each crossing are expressed in the form of:

] MTTS*0.039TOV * 0.411 -4.685[2)|(ˆ

++= eGYCE (5.68)

where 2

)|(ˆG

YCE - Number of Equivalent Fatalities expected to sustain at a crossing in

Group2 per 5 years.

b. GLM Negat ive Binomia l Regression Model

The Negative Binomial model reflects on the same variables, which were selected for

the above-mentioned Poisson model. However, the parameter estimation values on

these variables in the NB model show considerable changes from the Poisson model

(Table 5.67). Table 5.68 shows the goodness-of-fit details on the GLM Negative

Binomial Regression model.

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Table 5.67: Parameter Estimates of GLM Negative Binomial Model for Protection Type 2

Parameter B Std. Error

95% Wald Confidence

Interval Hypothesis Test

Lower Upper Wald Chi-Square df Sig.

(Intercept) -4.800 0.168 -5.129 -4.471 817.468 1 0.000

TOV 0.474 0.038 0.399 0.548 155.045 1 0.000

MTTS 0.039 0.003 0.034 0.045 221.841 1 0.000

(Scale) a

1

Dependent Variable: EFS

Model: (Intercept), TOV, MTTS

a - Fixed at the displayed value.

Table 5.68: Goodness-of-Fit Results of GLM Negative Binomial Model - Protection Type 2

Crossing Protection Type 2 Value df Value / df

Deviance 1730.5 4740 0.365

Scaled Deviance 1730.5 4740

Pearson Chi-Square 4264.0 4740 0.900

Scaled Pearson Chi-Square 4264.0 4740

Log Likelihood(a) -1486.1

Akaike's Information Criterion (AIC) 2978.2

Finite Sample Corrected AIC (AICC) 2978.2

Bayesian Information Criterion (BIC) 2997.6

Consistent AIC (CAIC) 3000.6

Dependent Variable: EFS

Model: (Intercept), TOV, MTTS

Consequences Predic t ion Equat ion of GLM Model (Nega t ive Binomia l Regression)

According to the NB model, the expected consequences (Equivalent Fatalities) per

accident for 5 years at each crossing are expressed in the form of:

] MTTS*0.039TOV * 0.474 -4.800[

2)|(ˆ++= eGYCE

(5.69)

where 2

)|(ˆG

YCE - Number of Equivalent Fatalities expected to sustain at a crossing in

Group2 per 5 years.

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Goodness-of-Fit Results and Comparisons betw een Poiss on and NB Models

By referring the goodness-of-fit values, the Poisson model yielded a Pearson Chi-

Square (value per degrees of freedom) to 1.008 suggesting a minor amount of over-

dispersion in the data (Table 5.66). The Negative Binomial model (Table 5.68) shows

a slightly better result in Pearson Chi-Square value (0.900). In comparison of the

Akaike's Information Criterion (AIC), the value of the NB model (2978.2) is smaller

than that of the Poisson model (3028.8). In addition, the values for mean and

variance of the accidental consequences data for Protection Type 2 crossings show

0.11 and 0.14 respectively. Since the Poisson model requires the mean and variance

to be equal, it is unsuitable for data with greater variance than mean. The Negative

Binomial may be more appropriate in such settings as its variance is always larger

than the mean. Based on these findings, the NB model is therefore considered to be

more appropriate than Poisson model in the initial process of consequences

prediction. The Empirical Bayesian model is then used with adjustment to the NB

model developed in order to enhance the quality of prediction.

c. Empirica l Bayesian Model (Adjustm ent to GLM NB Regression Model

Results)

Over-dispersion Parameter

Table 5.69: Over-Dispersion Parameter and Weighting Factors Estimation - EB Model

Crossing Protection Type 2

Mean of Consequences Estimated by NB Model - )(ˆ CE 0.0876

Variance of Consequences - )(CVar 0.1431

Over-Dispersion Parameter - κ 0.0536

Weighting Factor - 1ω 0.6203

Weighting Factor - 2ω 0.3797

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Consequences Predic t ion E quat ion of EB Model

2)|(ˆ*22)|(*12)]|(),|[(ˆGYCEGyCGyCYCE ωω +=

(5.70)

or:

] MTTS*0.039TOV * 0.474 -4.800[*3797.02)|(*6203.02)]|(),|[(ˆ

+++= eGyCGyCYCE (5.71)

where 2)|(

GyC - Number of Equivalent Fatalities sustained at a crossing in Group2 in

five-year history;

2)|(ˆ

GYCE - Number of Equivalent Fatalities (predicted by NB Model) expected to

sustain at a crossing in Group2 per 5 years; and

2)]|(),|[(ˆ

GyCYCE - Number of Equivalent Fatalities (predicted by EB Model which is

adjusted to the NB Model result) expected to sustain at a crossing in Group2 per 5

years.

Comparison of Goodness-of-Fit Results betw een EB and NB Models for Fina l

Select ion

A Chi-square goodness-of-fit test was separately applied to the test results obtained

by the NB and EB models for each of the explanatory variables. The Chi-square

goodness-of-fit values for maximum timetable train speed and total occupants in

vehicle are calculated and shown in Tables 5.70 and 5.71 respectively. For these

explanatory variables the calculated Chi-square values on the NB model showed

21.73 and 10.41 respectively. These results show that the NB model has Chi-square

values greater than the critical value (2

3,05.0χ = 7.82) at 5% level of significance. The

values on the EB model showed 3.96 and 1.79 respectively. The EB model has Chi-

square values less than the critical value. In comparison to calculated Chi-square

values, the EB model shows a better result than the NB model in all cases. In

addition, the EB model estimates the R-square (R2) value of 0.41. This means that

the model has explained 41% of the original variability, and is left with 59% residual

variability. In summary, even though this group of crossings (with Stop Signs or

Cross-bucks) suggested a minor problem of over-dispersion in the consequences

data, the EB model is more statistically acceptable for prediction of consequences.

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Table 5.70: Goodness-of-Fit Results of NB & EB Models - Max Timetable Train Speed

Maximum Time Table Train Speed

(mph)

Number of Observed Equivalent

Fatalities Used in Developing

Models

Predicted Number of Equivalent Fatalities for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

1 _ 40 113 134.60 122.08 3.47 0.68

41 _ 50 105 92.03 99.55 1.83 0.30

51 _ 60 170 137.28 156.25 7.80 1.21

Over 60 116 152.27 131.25 8.64 1.77

Grand Total 504 516.18 509.12 21.73 3.96

Critical Chi-Square Value ( 23,05.0χ ) 7.82 7.82

Table 5.71: Goodness-of-Fit Results of NB & EB Models - Total Occupants in Vehicle

Total Occupants in

Vehicle

Number of Observed Equivalent

Fatalities Used in Developing

Models

Predicted Number of Equivalent Fatalities for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

0 or 1 298 316.51 305.78 1.08 0.20

2 120 95.99 109.91 6.01 0.93

3 34 37.75 35.58 0.37 0.07

4 or More 52 65.93 57.86 2.94 0.59

Grand Total 504 516.18 509.12 10.41 1.79

Critical Chi-Square Value ( 23,05.0χ ) 7.82 7.82

Specific Calcula t ions for Consequences Pr edic t ion at Grade Crossings using EB

Model

Consider the crossing (ID No: 005129U) with the historical data of three (3)

equivalent fatalities per accident during the period 2001-2005; maximum timetable

train speed (90) and total occupants in vehicle (1); Using the Equation 5.69, the NB

model predicts the total consequences at this grade crossing in the five-year period

as:

] 90*0.0391 * 0.474 -4.800[)|(ˆ

005129U

++= eYCE = 0.46

From Table 5.69, the values of weighting factors are: =1ω 0.6203 and =2ω 0.3797.

By the Equation 5.70, the EB model predicts the total consequences at this grade

crossing in the five-year period as:

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=+= 46.0*3797.03*6203.0),(ˆ005129U

yYE 2.04

Similarly, the total consequences were estimated for each crossing in the group using

the NB and EB models and the relevant values were recorded. For example,

Table 5.72 reveals the top ten locations by consequences predicted with the EB

model in the group.

Table 5.72: Top Ten Locations by Consequence Predicted with EB Model in Protection

Type 2

Grade Crossing

ID

Equivalent Fatalities per

Accident in 5 Years

History

Prediction of Equivalent

Fatalities per Accident Using

NB Model (5 Years)

Prediction of Equivalent Fatalities

per Accident Using EB Model

(5 Years)

478073H 5 0.14 3.16

813642K 4 0.21 2.56

390642M 4 0.21 2.56

300152A 4 0.14 2.53

348428Y 4 0.09 2.52

636852M 4 0.06 2.51

005129U 3 0.46 2.04

637344B 3 0.21 1.94

731968X 3 0.14 1.91

525087V 3 0.14 1.91

5.5.2.3 Crossing Protection Type 3 (Signals, Bells or Warning Devices)

In the Protection Type 3 group of crossings, only 199 accidents resulted in

consequences with at least one equivalent fatality score during the 2001-2005 period

in the USA. Using the equation of ‘Equivalent Fatality Score’, a total of

248 equivalent fatalities were estimated in this group. There are only 2,723 records

considered suitable for model development once the other records, which have data

quality issues with variables, have been discarded. The value of 7 was recorded for

the maximum number of Equivalent Fatalities at a given crossing in this group.

Descriptive statistics of seven variables, which were considered to initiate the model

development, are summarised in Table 5.73.

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Table 5.73: Descriptive Statistics on Variables Used in the Model - Protection Type 3

Crossing Protection Type 3 Count Minimum Maximum Mean Std. Deviation

Equivalent Fatalities 2723 0 7 0.09 0.38

Maximum Timetable Train Speed 2723 1 90 32.94 18.74

Highway Speed 2723 1 105 13.59 15.27

Number of Main Tracks 2723 0 4 0.98 0.43

Number of Traffic Lanes 2723 1 9 2.51 1.13

Track Crossing Angle 2723 1 3 2.77 0.48

Total Occupants in Vehicle 2723 0 9 1.23 0.85

 

In the early part of modeling analysis in this group, Pearson correlation values for the

independent variables were estimated and shown in Table 5.74. As these variables

show reasonably low values in correlation, all of them were initially selected in the

process of model development.

Table 5.74: Pearson Correlation Between Variables Used in the Model - Protection Type 3

Crossing Protection

Type 3

Maximum Timetable Train

Speed

Highway Speed

Number of Main Tracks

Number of Traffic Lanes

Track Crossing

Angle

Total Occupants in

Vehicle

Maximum Timetable

Train Speed 1.00 -0.08 0.28 -0.28 0.07 -0.02

Highway Speed -0.08 1.00 -0.15 0.01 0.00 0.07

Number of Main Tracks 0.28 -0.15 1.00 -0.13 0.07 -0.03

Number of Traffic Lanes -0.28 0.01 -0.13 1.00 -0.08 0.05

Track Crossing Angle 0.07 0.00 0.07 -0.08 1.00 -0.02

Total Occupants in

Vehicle -0.02 0.07 -0.03 0.05 -0.02 1.00

a. GLM Poisson Regression Model

For the Poisson model, six independent variables were initially investigated. Two of

the six variables (maximum timetable train speed and total occupants in vehicle)

were found to be statistically significant at 5% level (Table 5.75). The discarded

variables were highway speed, number of main tracks, number of traffic lanes and

track crossing angle as their significance values showed more than 0.05. Table 5.76

shows the goodness-of-fit details on the GLM Poisson Regression model.

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Table 5.75: Parameter Estimates of GLM Poisson Regression Model - Protection Type 3

Parameter B Std. Error

95% Wald Confidence

Interval Hypothesis Test

Lower Upper Wald Chi-Square df Sig.

(Intercept) -4.449 0.176 -4.793 -4.105 641.082 1 0.000

TOV 0.424 0.040 0.346 0.502 114.488 1 0.000

MTTS 0.036 0.003 0.030 0.042 124.717 1 0.000

(Scale) a

1

Dependent Variable: EFS

Model: (Intercept), TOV, MTTS

a - Fixed at the displayed value

Table 5.76: Goodness-of-Fit Detais of GLM Poisson Regression Model - Protection Type 3

Crossing Protection Type 3 Value df Value / df

Deviance 1148.3 2720 0.422

Scaled Deviance 1148.3 2720

Pearson Chi-Square 3301.6 2720 1.214

Scaled Pearson Chi-Square 3301.6 2720

Log Likelihood(a) -785.4

Akaike's Information Criterion (AIC) 1576.7

Finite Sample Corrected AIC (AICC) 1576.7

Bayesian Information Criterion (BIC) 1594.4

Consistent AIC (CAIC) 1597.4

Dependent Variable: EFS

Model: (Intercept), TOV, MTTS

Consequences Predic t ion Equat ion of GLM Model (Poisson Regression)

According to the Poisson model, the expected consequences (Equivalent Fatalities)

per accident for 5 years at each crossing are expressed in the form of:

] MTTS*0.036TOV * 0.424 -4.449[3)/(ˆ

++= eGYCE (5.72)

where 3)|(ˆ

GYCE - Number of Equivalent Fatalities expected to sustain at a crossing in

Group3 per 5 years.

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263

b. GLM Negat ive Binomia l Regression Model

The Negative Binomial model reflects on the same variables, which were selected for

the above-mentioned Poisson model. However, the parameter estimation values on

these variables in the NB model show considerable changes from the Poisson model

(Table 5.77). Table 5.78 shows the goodness-of-fit details on the GLM Negative

Binomial Regression model.

Table 5.77: Parameter Estimates of GLM Negative Binomial Model - Protection Type 3

Parameter B Std. Error

95% Wald Confidence

Interval Hypothesis Test

Lower Upper Wald Chi-Square df Sig.

(Intercept) -4.410 0.196 -4.794 -4.026 506.391 1 0.000

TOV 0.415 0.053 0.311 0.518 61.322 1 0.000

MTTS 0.035 0.004 0.028 0.042 98.785 1 0.000

(Scale) a

1

Dependent Variable: EFS

Model: (Intercept), TOV, MTTS

a - Fixed at the displayed value.

Table 5.78: Goodness-of-Fit Results of GLM Negative Binomial Model - Protection Type 3

Crossing Protection Type 3 Value df Value / df

Deviance 940.8 2720 0.346

Scaled Deviance 940.8 2720

Pearson Chi-Square 3004.9 2720 1.105

Scaled Pearson Chi-Square 3004.9 2720

Log Likelihood(a) -767.4

Akaike's Information Criterion (AIC) 1540.8

Finite Sample Corrected AIC (AICC) 1540.8

Bayesian Information Criterion (BIC) 1558.5

Consistent AIC (CAIC) 1561.5

Dependent Variable: EFS

Model: (Intercept), TOV, MTTS

Consequences Predic t ion Equat ion of GLM Model (Nega t ive Binomia l Regression)

According to the NB model, the expected consequences (Equivalent Fatalities) per

accident for 5 years at each crossing are expressed in the form of:

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264

] MTTS*0.035TOV * 0.415 -4.410[

3)|(ˆ++= eGYCE

(5.73)

where 3)|(ˆ

GYCE - Number of Equivalent Fatalities expected to sustain at a crossing

inGroup3 per 5 years.

Goodness-of-Fit Results and Comparisons betw een Poiss on and NB Models

By referring the goodness-of-fit values, the Poisson model yielded a Pearson Chi-

Square (value per degrees of freedom) to 1.214 suggesting a minor amount of over-

dispersion in the data (Table 5.76). The Negative Binomial model shows (Table 5.78)

a slightly better result in Pearson Chi-Square value (1.105). In comparison of the

Akaike's Information Criterion (AIC), the value of the NB model (1540.8) is slightly

smaller than that of the Poisson model (1576.7). In addition, the values for mean and

variance of the accidental consequences data for Protection Type 3 crossings show

0.09 and 0.14 respectively. Since the Poisson model requires the mean and variance

to be equal, it is unsuitable for data with greater variance than mean. The Negative

Binomial may be more appropriate in such settings as its variance is always larger

than the mean. Based on these findings, the NB model is therefore considered to be

more appropriate than the Poisson model in the initial process of consequences

prediction. The Empirical Bayesian model is then used with adjustment to the NB

model developed in order to enhance the quality of prediction.

c. Empirica l Bayesian Model (Adjustm ent to GLM NB Regression Model

Results)

Over-dispersion Parameter

Table 5.79: Over-Dispersion Parameter and Weighting Factors Estimation - EB Model

Crossing Protection Type 3

Mean of Consequences Estimated by NB Model - )(ˆ CE 0.0749

Variance of Consequences - )(CVar 0.1453

Over-Dispersion Parameter - κ 0.0386

Weighting Factor - 1ω 0.6598

Weighting Factor - 2ω 0.3402

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265

Consequences Predic t ion E quat ion of EB Model

3)|(ˆ*23)|(*13)]|(),|[(ˆGYCEGyCGyCYCE ωω +=

(5.74)

or:

] MTTS*0.035TOV * 0.415 -4.410[*3402.03)|(*6598.03)]|(),|[(ˆ

+++= eGyCGyCYCE (5.75)

where 3)|(

GyC - Number of Equivalent Fatalities sustained at a crossing in Group3 in

five-year history;

3)|(ˆ

GYCE - Number of Equivalent Fatalities (predicted by NB Model) expected to

sustain at a crossing in Group3 per 5 years; and

3)]|(),|[(ˆ

GyCYCE - Number of Equivalent Fatalities (predicted by EB Model which is

adjusted to the NB Model result) expected to sustain at a crossing in Group3 per 5

years.

Comparison of Goodness-of-Fit Results betw een EB and NB Models for Fina l

Select ion

A Chi-square goodness-of-fit test was separately applied to the test results obtained

by the NB and EB models for each of the explanatory variables. The Chi-square

goodness-of-fit values for maximum timetable train speed and total occupants in

vehicle are calculated and shown in Tables 5.80 and 5.81 respectively. For these

explanatory variables the calculated Chi-square values on the NB model showed 7.25

and 0.63 respectively. The values on the EB model showed 1.05 and 0.09

respectively. These results show that both models have Chi-square values less than

the critical value (2

3,05.0χ = 7.82) at 5% level of significance. However, in comparison

of calculated Chi-square values, the EB model shows better result than the NB model

in all cases. In addition, the EB model estimates the R-square (R2) value of 0.45. This

means that the model has explained 45% of the original variability, and is left with

55% residual variability. In summary, even though this group of crossings (with

Signals, Bells or Warning Devices) suggested a minor problem of over-dispersion in

the consequences data, the EB model is more statistically acceptable for prediction of

consequences.

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Table 5.80: Goodness-of-Fit Results of NB & EB Models - Max Timetable Train Speed

Maximum Time Table Train Speed

(mph)

Number of Observed Equivalent

Fatalities Used in Developing

Models

Predicted Number of Equivalent Fatalities for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

1 _ 40 93 102.20 96.56 0.83 0.13

41 _ 50 57 44.16 52.04 3.73 0.47

51 _ 60 67 60.52 64.49 0.69 0.10

Over 60 31 39.93 34.45 2.00 0.35

Grand Total 248 246.81 247.54 7.25 1.05

Critical Chi-Square Value ( 23,05.0χ ) 7.82 7.82

Table 5.81: Goodness-of-Fit Results of NB & EB Models - Total Occupants in Vehicle

Total Occupants in

Vehicle

Number of Observed Equivalent

Fatalities Used in Developing

Models

Predicted Number of Equivalent Fatalities for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

0 or 1 152 155.55 153.37 0.08 0.01

2 49 44.10 47.11 0.54 0.08

3 15 15.20 15.08 0.00 0.00

4 or More 32 31.96 31.98 0.00 0.00

Grand Total 248 246.81 247.54 0.63 0.09

Critical Chi-Square Value ( 23,05.0χ ) 7.82 7.82

Specific Calcula t ions for Consequences Pr edic t ion at Grade Crossings using EB

Model

Consider the crossing (ID No: 725656B) with the historical data of two (2)

equivalent fatalities per accident during the period of 2001-2005; maximum

timetable train speed (79) and total occupants in vehicle (1); Using the Equation 5.73,

the NB model predicts the total consequences at this grade crossing in the five-year

period as:

] 79*0.0351 * 0.415 -4.410[)|(ˆ

725656B

++= eYCE = 0.30

From Table 5.79, the values of weighting factors are: =1ω 0.6598 and =2ω 0.3402.

By the Equation 5.74, the EB model predicts the total consequences at this grade

crossing in the five-year period as:

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267

=+= 30.0*3402.02*6598.0),(ˆ725656B

yYE 1.42

Similarly, the total consequences were estimated for each crossing in the group using

the NB and EB models and the relevant values were recorded. For example,

Table 5.82 reveals the top ten locations by consequences predicted with the EB

model in the group.

Table 5.82: Top Ten Locations by Consequence Predicted with EB Model in Protection

Type 3

Grade Crossing

ID

Equivalent Fatalities per

Accident in 5 Years

History

Prediction of Equivalent

Fatalities per Accident Using

NB Model (5 Years)

Prediction of Equivalent Fatalities

per Accident Using EB Model

(5 Years)

028394Y 7 0.30 4.72

732018G 5 0.11 3.34

715671B 5 0.10 3.33

300653E 4 0.30 2.74

481587S 4 0.15 2.69

719983X 3 0.15 2.03

841809U 3 0.15 2.03

725945C 3 0.03 1.99

072894M 2 0.30 1.42

725656B 2 0.30 1.42

5.5.2.4 Crossing Protection Type 4 (Gates or Full Barrier)

In the Protection Type 4 group of crossings, only 771 accidents resulted in

consequences with at least one equivalent fatality score during the 2001-2005 period

in the USA. Using the equation of ‘Equivalent Fatality Score’, a total of 878

equivalent fatalities were estimated in this group. There are only 5,441 records

considered suitable for model development once the other records, which have data

quality issues with variables, have been discarded. The value of 5 was recorded for

the maximum number of Equivalent Fatalities at a given crossing in this group.

Descriptive statistics of seven variables, which were considered to initiate the model

development, are summarised in Table 5.83.

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268

Table 5.83: Descriptive Statistics on Variables Used in the Model - Protection Type 4

Crossing Protection Type 4 Count Minimum Maximum Mean Std. Deviation

Equivalent Fatalities 5441 0 5 0.16 0.43

Maximum Timetable Train Speed 5441 5 90 51.52 19.73

Highway Speed 5441 1 90 8.57 12.89

Number of Main Tracks 5441 0 5 1.35 0.58

Number of Traffic Lanes 5441 1 9 2.52 1.10

Track Crossing Angle 5441 1 3 2.81 0.46

Total Occupants in Vehicle 5441 0 9 1.04 0.85

 

In the early part of modeling analysis in this group, Pearson correlation values for the

independent variables were estimated and shown in Table 5.84. As these variables

show reasonably low values in correlation, all of them were initially selected in the

process of model development.

Table 5.84: Pearson Correlation Between Variables Used in the Model - Protection Type 4

Crossing Protection

Type 4

Maximum Timetable Train

Speed

Highway Speed

Number of Main Tracks

Number of Traffic Lanes

Track Crossing

Angle

Total Occupants in

Vehicle

Maximum Timetable

Train Speed 1.00 -0.11 0.19 -0.10 0.03 -0.07

Highway Speed -0.11 1.00 -0.10 0.00 0.02 0.21

Number of Main Tracks 0.19 -0.10 1.00 0.00 0.02 -0.10

Number of Traffic Lanes -0.10 0.00 0.00 1.00 0.01 0.05

Track Crossing Angle 0.03 0.02 0.02 0.01 1.00 0.01

Total Occupants in

Vehicle -0.07 0.21 -0.10 0.05 0.01 1.00

a. GLM Poisson Regression Model

For the Poisson model, six independent variables were initially investigated. Two of

the six variables (maximum timetable train speed and total occupants in vehicle)

were found to be statistically significant at 5% level (Table 5.85). The discarded

variables were highway speed, number of main tracks, number of traffic lanes and

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269

track crossing angle as their significance values showed more than 0.05. Table 5.86

shows the goodness-of-fit details on the GLM Poisson Regression model.

Table 5.85: Parameter Estimates of GLM Poisson Regression Model - Protection Type 4

Parameter B Std. Error

95% Wald Confidence

Interval Hypothesis Test

Lower Upper Wald Chi-Square df Sig.

(Intercept) -3.575 0.137 -3.843 -3.308 685.576 1 0.000

TOV 0.433 0.033 0.369 0.497 174.275 1 0.000

MTTS 0.022 0.002 0.018 0.026 114.714 1 0.000

(Scale) a

1

Dependent Variable: EFS

Model: (Intercept), TOV, MTTS

a - Fixed at the displayed value

Table 5.86: Goodness-of-Fit Detail of GLM Poisson Regression Model - Protection Type 4

Crossing Protection Type 4 Value df Value / df

Deviance 2597.9 5438 0.478

Scaled Deviance 2597.9 5438

Pearson Chi-Square 4529.5 5438 0.833

Scaled Pearson Chi-Square 4529.5 5438

Log Likelihood(a) -2417.6

Akaike's Information Criterion (AIC) 4841.3

Finite Sample Corrected AIC (AICC) 4841.3

Bayesian Information Criterion (BIC) 4861.1

Consistent AIC (CAIC) 4864.1

Dependent Variable: EFS

Model: (Intercept), TOV, MTTS

Consequences Predic t ion Equat ion of GLM Model (Poisson Regression)

According to the Poisson model, the expected consequences (Equivalent Fatalities)

per accident for 5 years at each crossing are expressed in the form of:

] MTTS*0.022TOV *0.433 -3.575[

4)|(ˆ++= eGYCE

(5.76)

where 4)|(ˆ

GYCE - Number of Equivalent Fatalities expected to sustain at a crossing in

Group 4 per 5 years.

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270

b. GLM Negat ive Binomia l Regression Model

The Negative Binomial model reflects on the same variables, which were selected for

the above-mentioned Poisson model. However, the parameter estimation values on

these variables in the NB model show considerable changes from the Poisson model

(Table 5.87). Table 5.88 shows the goodness-of-fit details on the GLM Negative

Binomial Regression model.

Table 5.87: Parameter Estimates of GLM Negative Binomial Model for Protection Type 4

Parameter B Std. Error

95% Wald Confidence

Interval Hypothesis Test

Lower Upper Wald Chi-Square df Sig.

(Intercept) -3.548 0.126 -3.795 -3.301 790.977 1 0.000

TOV 0.403 0.026 0.352 0.454 239.072 1 0.000

MTTS 0.022 0.002 0.019 0.026 137.839 1 0.000

(Scale) a

1

Dependent Variable: EFS

Model: (Intercept), TOV, MTTS

a - Fixed at the displayed value.

Table 5.88: Goodness-of-Fit Results of GLM Negative Binomial Model - Protection Type 4

Crossing Protection Type 4 Value df Value / df

Deviance 3232.4 5438 0.594

Scaled Deviance 3232.4 5438

Pearson Chi-Square 5303.9 5438 0.975

Scaled Pearson Chi-Square 5303.9 5438

Log Likelihood(a) -2416.1

Akaike's Information Criterion (AIC) 4838.3

Finite Sample Corrected AIC (AICC) 4838.3

Bayesian Information Criterion (BIC) 4858.1

Consistent AIC (CAIC) 4861.1

Dependent Variable: EFS

Model: (Intercept), TOV, MTTS

Consequences Predic t ion Equat ion of GLM Model (Nega t ive Binomia l Regression)

According to the NB model, the expected consequences (Equivalent Fatalities) per

accident for 5 years at each crossing are expressed in the form of:

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271

] MTTS*0.022TOV *0.403 -3.548[

4)|(ˆ++= eGYCE

(5.77)

where 4)|(ˆ

GYCE - Number of Equivalent Fatalities expected to sustain at a crossing in

Group 4 per 5 years.

Goodness-of-Fit Results and Comparisons betw een Poiss on and NB Models

By referring the goodness-of-fit values, the Poisson model yielded a Pearson Chi-

Square (value per degrees of freedom) to 0.833 suggesting a minor amount of under-

dispersion in the data (Table 5.86).The Negative Binomial model (Table 5.88) shows

a slightly better result in Pearson Chi-Square value (0.975). In comparison of the

Akaike's Information Criterion (AIC), the value of the NB model (4838.3) is slightly

smaller than that of the Poisson model (4841.3). In addition, the values for mean and

variance of the accidental consequences data for Protection Type 4 crossings show

0.16 and 0.18 respectively. Since the Poisson model requires the mean and variance

to be equal, it is unsuitable for data with greater variance than mean. The Negative

Binomial may be more appropriate in such settings as its variance is always larger

than the mean. Based on these findings, the NB model is therefore considered to be

more appropriate than the Poisson model in the initial process of consequences

prediction. The Empirical Bayesian model is then used with adjustment to the NB

model developed in order to enhance the quality of prediction.

c. Empirica l Bayesian Model (Adjustm ent to GLM NB Regression Model

Results)

Over-dispersion Parameter

Table 5.89: Over-Dispersion Parameter and Weighting Factors Estimation - EB Model

Crossing Protection Type 4

Mean of Consequences Estimated by NB Model - )(ˆ CE 0.1486

Variance of Consequences - )(CVar 0.1890

Over-Dispersion Parameter - κ 0.1169

Weighting Factor - 1ω 0.5598

Weighting Factor - 2ω 0.4402

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Consequences Predic t ion E quat ion of EB Model

4)|(ˆ*24)|(*14)]|(),|[(ˆGYCEGyCGyCYCE ωω +=

(5.78)

or:

] MTTS*0.022TOV *0.403 -3.548[*4402.04)|(*5598.04)]|(),|[(ˆ

+++= eGyCGyCYCE (5.79)

where 4)|(

GyC - Number of Equivalent Fatalities sustained at a crossing in Group4 in 5

years history;

4)|(ˆ

GYCE - Number of Equivalent Fatalities (predicted by NB Model) expected to

sustain at a crossing in Group4 per 5 years; and

4)]|(),|[(ˆ

GyCYCE - Number of Equivalent Fatalities (predicted by EB Model which is

adjusted to the NB Model result) expected to sustain at a crossing in Group4 per 5

years.

Comparison of Goodness-of-Fit Results betw een EB and NB Models for Fina l

Select ion

A Chi-square goodness-of-fit test was separately applied to the test results obtained

by the NB and EB models for each of the explanatory variables. The Chi-square

goodness-of-fit values for maximum timetable train speed and total occupants in

vehicle are calculated and shown in Tables 5.90 and 5.91 respectively. For these

explanatory variables the calculated Chi-square values on the NB model showed 9.26

and 6.16 respectively. These results show that the NB model has the Chi-square

value greater than the critical value (2

3,05.0χ = 7.82) at 5% level of significance for

maximum timetable train speed and lower than the critical value for total occupants

in vehicle. The values on the EB model showed 1.92 and 1.52 respectively. The EB

model has Chi-square values less than the critical value. In comparison of calculated

Chi-square values, the EB model shows better result than the NB model in all cases.

In addition, the EB model estimates the R-square (R2) value of 0.35. This means that

the model has explained 35% of the original variability, and is left with 65% residual

variability. In summary, even though this group of crossings (with Gate or Full

Barrier) suggested a minor problem of under-dispersion in the consequence data, the

EB model is more statistically acceptable for prediction of consequences.

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Table 5.90: Goodness-of-Fit Results of NB & EB Models - Max Timetable Train Speed

Maximum Time Table Train Speed

(mph)

Number of Observed Equivalent

Fatalities Used in Developing

Models

Predicted Number of Equivalent Fatalities for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

1 _ 40 158 170.60 163.80 0.93 0.21

41 _ 50 150 131.91 141.67 2.48 0.49

51 _ 60 228 202.35 216.19 3.25 0.65

Over 60 342 373.14 356.34 2.60 0.58

Grand Total 878 878.00 878.00 9.26 1.92

Critical Chi-Square Value ( 23,05.0χ ) 7.82 7.82

Table 5.91: Goodness-of-Fit Results of NB & EB Models - Total Occupants in Vehicle

Total Occupants in

Vehicle

Number of Observed Equivalent

Fatalities Used in Developing

Models

Predicted Number of Equivalent Fatalities for 5 Years Period

Calculated Chi-Square Goodness of Fit Value

Negative Binomial Model

Empirical Bayesian Model

Negative Binomial Model

Empirical Bayesian Model

0 or 1 628 618.94 623.83 0.13 0.03

2 136 129.22 132.88 0.36 0.07

3 66 62.63 64.45 0.18 0.04

4 or More 48 67.22 56.85 5.49 1.38

Grand Total 878 878.00 878.00 6.16 1.52

Critical Chi-Square Value ( 23,05.0χ ) 7.82 7.82

Specific Calcula t ions for Consequences Pr edic t ion at Grade Crossings using EB

Model

Consider the crossing (ID No: 500307S) with the historical data of three (3)

equivalent fatalities per accident during the period of 2001-2005; maximum

timetable train speed (80) and total occupants in vehicle (1); Using the Equation 5.77,

the NB model predicts the total consequences at this grade crossing in the five-year

period as:

] 80*0.0221 *0.403 -3.548[)|(ˆ500307S

++= eYCE = 0.26

From Table 5.89, the values of weighting factors are: =1ω 0.5598 and =2ω 0.4402.

By the Equation 5.78, the EB model predicts the total consequences at this grade

crossing in the five-year period as:

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=+= 26.0*4402.03*5598.0),(ˆ500307S

yYE 1.79

Similarly, the total consequences were estimated for each crossing in the group using

the NB and EB models and the relevant values were recorded. For example,

Table 5.92 reveals the top ten locations by consequences predicted with the EB

model in the group.

Table 5.92: Top Ten Locations by Consequence Predicted with EB Model in Protection

Type 4

Grade Crossing

ID

Equivalent Fatalities per

Accident in 5 Years

History

Prediction of Equivalent

Fatalities per Accident Using

NB Model (5 Years)

Prediction of Equivalent Fatalities

per Accident Using EB Model

(5 Years)

538717A 5 0.16 2.87

724758R 5 0.13 2.86

082926T 4 0.23 2.34

066762N 4 0.13 2.30

017314X 4 0.13 2.30

300207K 4 0.10 2.29

500307S 3 0.26 1.79

629688U 3 0.25 1.79

013796L 3 0.25 1.79

746784S 3 0.25 1.79

5.6 Summary

The chapter presented details of all three common types of accident and

consequences prediction models (Poisson, Negative Binomial and Empirical

Bayesian models). The models were developed using accident data of USDOT FRA

occurrence database and distinguished with four distinctive expressions of types of

protection (i.e. 1. No Signs or No signals / 2. Stop Signs or Cross-bucks / 3. Signals,

Bells or Warning Devices / 4. Gates or Full Barrier) and were tested for their

goodness-of-fit.

The details of models development process, based on critical, significant and

appropriate explanatory variables are described and outlined. In this process, models

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to predict accident frequencies and accidental consequences at railway-highway

grade crossings are proposed and described first. The process adopted includes two

stages: Firstly, the development of a set of accident prediction models that are

validated using a comprehensive data for the USA accidents data. Secondly, the

same procedure is used to identify the most appropriate accidental consequences

models. All distinctive accident frequency and accidental consequences prediction

models are developed for each group of the four protection types of crossings. For

the prediction of accident frequencies at the grade crossings, a GLM Poisson

Regression model and a GLM Negative Binomial Regression model are separately

generated (using SPSS V15 software with appropriate explanatory variables) for the

crossings with the first type of protection. By comparison of goodness-of-fit values

of these two models, the NB model showed better results than the Poisson model and

was selected for further enhancement on the quality of accident prediction. This

means that the GLM Poisson Model is considered to be not suitable for this case. The

Empirical Bayesian model was then generated with adjustment to the NB model. By

comparison of goodness-of-fit values of the EB and NB models, the EB model was

found to be more suitable than the NB model and was selected for accident

prediction for crossings with the first type of protection. These model selection

procedure steps were repeated for crossings with the remaining three types of

protections. The same model selection procedure for predicting accident frequencies

was also used for estimating accidental consequences for each type of protection. In

all cases, the EB model showed better results than the other models and was selected

for both the accident prediction and the accidental consequences estimation. These

preferred models form the basis for assessing risk at each railway-highway grade

crossing and in identifying black-spots among those crossings in detail as presented

in the following chapter.

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Chapter 6

Development of Safety Risk Index (SRI) for Risks Assessment at Grade Crossings

6.0 Introduction

A safety risk index is a useful method / technique as a standardised measure for

assessing and prioritising risks at grade crossings across large rail infrastructures of

diverse geographical locations. Given safety risk at rail crossings is directly related

to accidents and consequences, models for predicting accidents and consequences at

railway crossings developed and presented earlier form the basis of developing an

overall model of safety risk index. Since the development of models for predicting

accidents and consequences focuses on four protection types as identified earlier, the

development of a model for safety risk index aims to provide a measure that enables

assessing and prioritising risks associated with those protection types. Therefore, the

main objective of developing a safety risk index is to provide a standardised measure

across those protection types for assessing and prioritising risks at grade crossings.

In the overall process of model development, the previous chapter presented models

for predicting distinctive accident frequency and accidental consequences for each of

the four protection types of grade crossings. These models assist in assessing risk at

each railway-highway grade crossing and would also enable identifying the worst

performing crossings in relations to safety. In this chapter, steps, procedures and

approaches involved in the construction of Safety Risk Index (SRI) for assessing and

prioritising the safety risks at railway grade crossings are introduced, described and

illustrated. A key aspect of the model development at this stage is that appropriate

factors and variables (which influence safety risks at grade crossings) are combined

into one simple quantitative measurable index to quantify and assess safety. By

integrating the predicted values for accident frequency and accidental consequences

from the models developed in the previous chapter, a safety risk index score for each

grade crossing is evaluated. With the aid of these scores, the safety risk at grade

crossings is assessed and the black-spots grade crossings are then identified.

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This chapter is structured as follows. Firstly, background of the safety risk index

model (SRI) is presented, identifying key aspects and relationships between the

accidents frequency and accidental consequences prediction. The Safety Risk Index

model is then illustrated using an estimation of scores at each grade crossing and

graphical representation of the scores. Finally, the combined scores and graphical

representation of scores are used to assess safety risk at each rail crossing and to

identify black-spots. This is followed by a summary.

6.1 Development of Safety Risk Index (SRI) Model

As indicated in the chapter introduction, the main aim of this research is to develop a

quantitative risk analysis based methodology for assessing and comparing railway-

highway grade crossings in terms of safety risks, and then to identify the crossings

with unacceptably higher risks. The group of higher risk grade crossings are known

as “black-spot” crossings (as explained in Chapter 3). In order to assess the risk at

each crossing and to identify the black-spots, a quantitative index (Safety Risk Index)

is developed where steps involved in developing the index are outlined below.

6.1.1 Defining Safety Risk Index (SRI)

Estimations of accident frequencies and consequences for grade crossings in each

protection type discussed and presented earlier showed that some crossings had low

prediction of accident frequencies with high prediction of accidental consequences.

In other cases, some crossings had high prediction of accident frequencies with low

prediction of accidental consequences. However, the majority of the crossings had

low value predicted for both frequencies and consequences and very few had high

estimations for both indicators. In this case, combination of these two estimations

can be used to develop an approach to calculate the safety risks at grade crossings, as

illustrated in Figure 6.1. This approach of using the product of accident frequency

and accidental consequences estimations forms the basis for providing risk

assessment at each crossing by means of a “Safety Risk Index (SRI)”. In this method

the Safety Risk Index (ℜ ) directly measures the number of equivalent fatalities, as

shown below. For a given grade crossing, the Safety Risk Index (ℜ ) is defined as:

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Fatalities Equivalent

Accidents ofNumber

Fatalities Equivalent*Accidents ofNumber

esConsequenc Estimated *AccidentsEstimated )(Index Risk Safety

===ℜ

Estimation of Accident Frequency ( )(ˆ YE ) obtained from Chapter 5

Estimation of Consequences per Accident ( )|(ˆ YCE ) obtained from Chapter 5

Computation ofSafety Risk Index [ ℜ = )(ˆ YE * )|(ˆ YCE ]

Figure 6.1: Flow Diagram of Developing Safety Risk Index (SRI) Model

6.1.2 Identifying Safety Status of a Crossing using Graphical

Method

Based on the recognition of graphical methods being developed and widely used in

the past for assessing the risk at grade crossings with identification of Black-Spots,

this research adapts and extends Saccomanno et al. (2003)’s work by allowing

different values for accident frequency and accidental consequences, as opposed to

equal importance in the original model. Thus, an improved quantitative risk

assessment approach was developed where the two key indicators (accidents

frequency and accidental consequences) are combined together to provide a single

risk measure. A two-dimensional graphical representation is adopted, in order to

assess the safety risks at grade crossings. This approach locates grade crossings in a

two-dimensional graph with their safety risks status (including estimated accidents

and estimated consequences). For example, Figure 6.2 shows a typical two-

dimensional graph for identifying the safety status of grade crossings. Estimated

accidents over five years (X) and estimated consequences (Y) are displayed on the

x-axis and y-axis of the graph respectively. Each point plotted on the graph

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represents the safety risk status of an individual crossing. By plotting points for each

crossing on the graph for all four types of protection separately, the safety risk status

of each crossing can be depicted. From the graph, the black-spots can then be

conveniently identified in the relevant crossings protection type. By definition, a

Safety Risk Index is defined as:

  Y*X)(IndexRisk Safety =ℜ

Identifying Safety Risk Status of a Crossing by Severity Risk Index Graph

Number of Predicted Accidents per Year (X)

Pre

dict

ed C

onse

quen

ces

(Y)

(Equ

ival

ent F

atal

ities

per

Acc

iden

t)

Severity Risk Status Position of a Crossing Concerned Severity Risk Index Curve (X*Y = R)

Figure 6.2: Identifying Safety Status of Grade Crossings using Safety Risk Index Curve

Consider the equation of X*Y = ℜ which represents a typical set of power decay

curves, where the values of X and Y can vary while “ℜ ” remains a constant value

which will depends on the safety risk status of a crossing concerned. This curve is

known as the “Safety Risk Index Curve” and can be illustrated by point ‘A’ being on

the Safety Risk Index Curve (C) as shown in Figure 6.2 which represents the safety

status of a particular or concerned grade crossing. The risk value of the crossing (ℜ )

is given by ℜ = X*Y. It is therefore obvious that all crossings having the same safety

risk index values should fall on the same curve (C). This approach logically

demonstrates that dangerous crossings will have higher values of “ℜ ” and moderate

or safer crossings will have values lower than ℜ . The sensitivity of this curve is

explained in the following section.

A

At Point ‘A’ on Safety Risk Index Curve,

Safety Risk Index value of a crossing (ℜ ) is given by ℜ = X*Y

X

Y

Safety Risk Index Curve ‘C’

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6.2 Identifying Black-Spots (C rossings with Unacceptable

Higher Safety Risk Index Values)

As stated earlier, the group of grade crossings which have higher (unacceptable)

safety risk values are known as “black-spot” crossings. The safety risk index values

play a vital role in identifying these black-spots.

6.2.1 Introducing Threshold Curves of Safety Risk Index

Consider three safety risk index curves shown in Figure 6.3 with different SRI values

1ℜ , 2ℜ and 3ℜ (provided 1ℜ < 2ℜ < 3ℜ ). The crossings having safety risk index

values of 1ℜ fall on the curve ‘C1’. In a similar manner, the crossings having safety

risk index values of 2ℜ and 3ℜ will fall on the curves ‘C2’ and ‘C3’ respectively.

Because of 1ℜ < 2ℜ < 3ℜ , by definition it can be considered that the crossings

represented by the curve ‘C3’ are more dangerous than others represented by either

the curve ‘C1’ or ‘C2’.

Safety Risk Index Curves with Different SRI Values

Number of Predicted Accidents per Year (X)

Pre

dict

ed C

onse

quen

ces

(Y)

(Equ

ival

ent F

atal

ities

per

Acc

iden

t)

Safety Risk Index Curve C1 Safety Risk Index Curve C2 Safety Risk Index Curve C3

Figure 6.3: Safety Risk Index Curves with Different SRI Values

SRI value (ℜ ) increases upwards

X*Y=3ℜ

X*Y=2ℜ

X*Y=1ℜ

SRI value (ℜ ) decreases downwards

1ℜ <

2ℜ < 3ℜ

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However, the crossings represented by the curve ‘C1’ are safer. The crossings falling

on the curve ‘C2’ will be moderate in safety. In fact, the safety of a crossing depends

on the value of ℜ . As the value of ℜ increases, the safety status of the crossings

becomes more dangerous. When “ℜ ” takes its optimal value or minimum

unacceptable value (0ℜ ), the Safety Risk curve becomes a “Safety Risk Index

Threshold” curve (X*Y = 0ℜ ). In other words, the threshold curve is a reference

curve which retains the minimum unacceptable risk index value of a crossing. It is

therefore noted that dangerous crossings (black-spots) should fall on or above the

threshold curve (X*Y = 0ℜ ) in the safety risk index graph. The crossings falling

below the threshold curve are assumed to be reasonably safer than others.

6.2.2 Selecting Safety Ri sk Index Threshold Value

To determine the optimal value for threshold curves requires clear and considerable

explanations. Basically, this critical value relates to the number of crossings

suggested to enhance safety at minimal cost of intervention. Of course, the number of

crossings depends on budgetary constraints set by the relevant authorities. Therefore

a great deal of study on cost benefit analysis while considering several

countermeasures for intervention will be needed to determine the critical value of the

threshold for each protection type of crossing. See example in Figure 6.4 for

estimating the threshold value for black-spots identification.

In general, the relationship between the safety risk levels and the percentage of

crossings which experienced accidents is expressed in the form of an exponential

decay curve as shown in the Figure. Meanwhile, it can be assumed that the

intervention cost to enhance safety at crossings linearly depends on the number of

crossings concerned. For example, consider if funds 0F are currently available and

allocated by the authorities for safety enhancement at grade crossings. Point “A”

indicates the value of 0F on the axis of intervention cost. Construct the horizontal

line “BA” through the point “A”, which meets the line of ‘Intervention cost to

enhance safety’ (BF) at the point “B” as shown on the figure. Draw the vertical line

“BC”, which meets the X-axis of ‘Percentage of crossings experienced with

accidents’ at the point “C”. The maximum number of crossings (0N ) for safety

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intervention can then be decided at point “C”. Similarly, construct the vertical line

“CD” which meets the curve of ‘Safety risk level of crossings’ at the point “D”.

Finally, draw the horizontal line “DE” which meets the Y-axis of ‘Safety risk level’

at the point “E”. The optimum value for Safety Risk Index Threshold (0ℜ ) is to be

determined at point “E”.

Estimating Threshold Value for Black-spots Identification

Percentage of Crossings Experienced w ith Accidents

Saf

ety

Ris

k Le

vel

Inte

rven

tion

Cos

t ($)

Intervention Cost ($) to Enhance Safety Safety Risk Level of Crossings

Cut-off Line

Optimum Safety Risk Index Value (

oℜ ) Achievable

Number of Crossings (oN )

need to be Enhanced in Safety at Available Fund

Available Fund for Safety Intervention (

oF )

E D

A

B

C

F

Figure 6.4: Estimating Threshold Value for Black-Spots Identification

However, as this type of cost benefit analysis (as shown in the above demonstration

in Figure 6.4) is not feasibly available at this stage in the study, an alternative method

is introduced to choose the critical value in this study. The Safety Risk Index values

of crossings within a protection type are initially calculated. The standardised scores

for all Safety Risk Indexes are then computed. Finally, the number of high risk

crossings are identified at various standardised score levels (such as 2, 3, 4 and so

on). This procedure is repeated for all types of protection. The relationship between

the standardised scores and the number of black-spot crossings is individually

identified and summarised in all types of protections (Figure 6.5).

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2 3 4 5 6

Protection Type 1 5 3 3 2 2

Protection Type 2 401 193 136 78 54

Protection Type 3 178 77 76 39 36

Protection Type 4 426 242 148 91 61

Grand Total 1010 515 363 210 153

0

200

400

600

800

1000

1200

Num

ber o

f Bla

ck-s

pots

Iden

tifie

d

Standardized Score of Severity Risk Index

Number of Black-spots by Protection Types Vs Standardized Score of SRI

Figure 6.5: Number of Black-Spots by Protection Types Vs Standardised Score of SRI

Table 6.1: Summary of Proposed Threshold Critical Values by Protection Types

Protection Type

of Grade

Crossings

Mean of Safety

Risk Index

Standard Deviance

of Safety Risk

Index

Reference

Standardized

Score

Threshold Critical

Value

1 0.0053 0.0367 4 0.15

2 0.0079 0.0326 4 0.14

3 0.0070 0.0380 4 0.16

4 0.0120 0.0376 4 0.16

It is therefore clearly noted that the number of black-spots identified entirely depends

on the standardised scores associated with the Safety Risk Index. For example, if the

score of 2 is selected, a total of 1,010 crossings are identified as black-spots within

all four protection types. The number of black-spots drops to 515 for the score of 3

and to 363 for score of 4 and so on. A further investigation and analysis is needed to

improve this relationship using budgetary constraints information, in order to

enhance the safety at grade crossings. In the absence of this information at this stage

of analysis, and for the purpose of demonstration, the value of the Safety Risk Index

that relates to the standardised score of 4 has been adopted as a threshold value in

this study. The proposed threshold values for each type of protections are

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summarised in the Table 6.1. Following is an illustration showing how the critical

threshold values are obtained. Consider Protection Type 1 crossings. The threshold

value for this type is calculated by the equation of:

deviance Standard

)Mean value - valueCritical (Threshold 4 of valueat the score edStandardis =

Mean valuedeviance Standardx4 valueCritical Threshold +=

15.0

0367.0*40053.0 valueCritical Threshold

=+=

6.2.3 Identifying Bl ack-Spots in Each Protection Type

Table 6.1 shows that for the common reference standardised score of 4, Protection

types 1, 2, 3 and 4 yielded the threshold critical values of 0.15, 0.14, 0.16 and 0.16

respectively. Using the average of these critical values, the common threshold can

assign the value of 0.15 approximately. In this study black-spots are therefore

identified with respect to a common threshold critical value of 0.15 in all types of

protection. This means that grade crossings with the estimated risk value of 0.15

equivalent fatalities or more over one year period are considered as black-spots. The

accidental grade crossings from each protection types are plotted separately in order

to compare them and to determine the black-spots in each group. Details of these

black-spots are listed and summarised in Table 6.6.

6.2.3.1 Crossing Protection Type 1 (No Signs or No signals)

From the data analysis it is noted that only 3 crossings (1.37% of all accidental

crossings in Protection Type 1) are estimated with a Safety Risk Index value more

than 0.15 as shown in Figure 6.6.

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SRI Vs Percentage of Crossings Experienced w ith Accidents - Prote ction Type 1

98.63

0.91

0.46

0.00 25.00 50.00 75.00 100.00

Less than 0.15

Betw een 0.15 and 0.30

More than 0.30

Saf

ety

Ris

k In

dex

(Equ

ival

ent F

atal

ities

per

Yea

r)

Percentage of Grade Crossings Experienced w ith Accidents

Figure 6.6: Safety Risk Index Vs Percentage of Protection Type 1 Accidental Crossings

Identifying Black-Spots Using SRI Threshold Curve - Protection Type 1

Severity Risk Threshold CurveX*Y = 0.15

0.00

0.50

1.00

1.50

2.00

0.00 0.10 0.20 0.30 0.40 0.50

Predicted Accidents per Year (X)

Pre

dict

ed E

quiv

alen

t Fat

aliti

es p

er A

ccid

ent (

Y)

3 Crossings (with Severity Risk Value over 0.15) which fall above the Threshold Curve are considered as Black-Spots in this Group

Grade Crossing (ID No.: 632469J) at Highest Riskwith Severity Risk Value of 0.43

Figure 6.7: Black-Spots Identification in Protection Type 1 Grade Crossings

In Figure 6.7, the safety status of individual crossings is plotted by estimated

accidents (X) and estimated consequences (Y) of the relevant crossings. In the same

graph, using the suggested critical value of 0.15, the threshold curve is also plotted.

The same plotting procedure will apply later to the other protection types. By looking

at the crossings in this group which fall on or above the threshold curve, only

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3 crossings are identified as black-spots and the details are summarised in Table 6.2.

In the same manner, the black-spots in other types of protection are identified and

their details are summarised.

Table 6.2: List of 3 Black-Spots Identified in Protection Type 1

Crossing ID Number

Number of Collisions Predicted per Year (X)

Consequences Predicted per an Accident (Y)

Severity Risk Index

632469J 0.28 1.51 0.43

022694S 0.36 0.72 0.26

361331H 0.25 0.72 0.18

6.2.3.2 Crossing Protection Type 2 (Stop Signs or Cross-bucks)

The analysis shows that 129 crossings (1.39 % of all accidental crossings in

Protection Type 2) are calculated with a Safety Risk Index value more than 0.15

(Figure 6.8).

 

 

 

SRI Vs Percentage of Crossings Experienced w ith Accidents - Protection Type 2

98.61

1.14

0.25

0.00 25.00 50.00 75.00 100.00

Less than 0.15

Betw een 0.15 and 0.30

More than 0.30

Saf

ety

Ris

k In

dex

(Equ

ival

ent F

atal

ities

per

Yea

r)

Percentage of Grade Crossings Experienced w ith Accidents

Figure 6.8: Safety Risk Index Vs Percentage of Protection Type 2 Accidental Crossings

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Identifying Black-Spots Using SRI Threshold Curve - Protection Type 2

Severity Risk Threshold CurveX*Y = 0.15

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0.00 0.25 0.50 0.75 1.00

Predicted Accidents per Year (X)

Pre

dict

ed E

quiv

alen

t Fat

aliti

es p

er A

ccid

ent (

Y)

129 Crossings (with Severity Risk Value over 0.15) which fall above the Threshold Curve are considered as Black-Spots in this

Grade Crossing (ID No.: 300182S) at Highest Riskwith Severity Risk Value of 0.77

Figure 6.9: Black-Spots Identification in Protection Type 2 Grade Crossings Figure 6.9 shows the safety status of grade crossings plotted. A total of 129 crossings

are identified as black-spots and details of the top five are summarised in Table 6.3.

Table 6.3: List of Top Five within 129 Black-Spots Identified in Protection Type 2

Crossing ID Number

Number of Collisions Predicted per Year (X)

Consequences Predicted per an Accident (Y)

Severity Risk Index

300182S 0.57 1.35 0.77

731968X 0.28 1.91 0.53

329012H 0.25 1.90 0.48

622318S 0.34 1.35 0.46

014877P 0.24 1.90 0.45

6.2.3.3 Crossing Protection Type 3 (Signals, Bells or Warning Devices)

The analysis shows that 76 crossings (1.35 % of all accidental crossings in Protection

Type 3) are calculated with a Safety Risk Index value more than 0.15 (Figure 6.10).

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SRI Vs Percentage of Crossings Experienced w ith Accidents - Protection Type 3

98.65

0.94

0.41

0.00 25.00 50.00 75.00 100.00

Less than 0.15

Betw een 0.15 and 0.30

More than 0.30

Saf

ety

Ris

k In

dex

(Equ

ival

ent F

atal

ities

per

Yea

r)

Percentage of Grade Crossings Experienced w ith Accidents

Figure 6.10: Safety Risk Index Vs Percentage of Protection Type 3 Accidental Crossings Figure 6.11 shows the safety status of grade crossings plotted. A total of 76 crossings

are identified as black-spots and details of the top five are summarised in Table 6.4.

Identifying Black-Spots Using SRI Threshold Curve - Protection Type 3

Severity Risk Threshold CurveX*Y = 0.15

0.00

1.00

2.00

3.00

4.00

5.00

0.00 0.50 1.00 1.50

Predicted Accidents per Year (X)

Pre

dict

ed E

quiv

alen

t Fat

aliti

es p

er A

ccid

ent (

Y)

76 Crossings (with Severity Risk Value over 0.15) which fall above the Threshold Curve are considered as Black-Spots in this Group

Grade Crossing (ID No.: 028394Y) at Highest Riskwith Severity Risk Value of 1.20

Figure 6.11: Black-Spots Identification in Protection Type 3 Grade Crossings

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289

Table 6.4: List of Top Five within 76 Black-Spots Identified in Protection Type 3

Crossing ID Number

Number of Collisions Predicted per Year (X)

Consequences Predicted per an Accident (Y)

Severity Risk Index

028394Y 0.26 4.72 1.20

794960S 0.48 1.36 0.65

640124J 0.85 0.69 0.59

352066W 0.38 1.37 0.52

478051H 0.76 0.67 0.52

6.2.3.4 Crossing Protection Type 4 (Gates or Full Barrier)

The analysis shows that 239 crossings (2.16 % of all accidental crossings in

Protection Type 4) are calculated with a Safety Risk Index value more than 0.15

(Figure 6.12).

 

 

 

SRI Vs Percentage of Crossings Experienced w ith Accidents - Protection Type 4

97.84

1.83

0.32

0.00 25.00 50.00 75.00 100.00

Less than 0.15

Betw een 0.15 and 0.30

More than 0.30

Saf

ety

Ris

k In

dex

(Equ

ival

ent F

atal

ities

per

Yea

r)

Percentage of Grade Crossings Experienced w ith Accidents

Figure 6.12: Safety Risk Index Vs Percentage of Protection Type 4 Accidental Crossing

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Identifying Black-Spots Using SRI Threshold Curve - Protection Type 4

Severity Risk Threshold CurveX*Y = 0.15

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00 0.25 0.50 0.75 1.00

Predicted Accidents per Year (X)

Pre

dict

ed E

quiv

alen

t Fat

aliti

es p

er A

ccid

ent (

Y)

239 Crossings (with Severity Risk Value over 0.15) which fall above the Threshold Curve are considered as Black-Spots in this Group

Grade Crossing (ID No.: 628171P) at Highest Riskwith Severity Risk Value of 0.88

Figure 6.13: Black-Spots Identification in Protection Type 4 Grade Crossings Figure 6.13 shows the safety status of grade crossings plotted. A total of

239 crossings are identified as black-spots and details of the top five are summarised

in Table 6.5.

Table 6.5: List of Top Five within 239 Black-Spots Identified in Protection Type 4

Crossing ID Number

Number of Collisions Predicted per Year (X)

Consequences Predicted per an Accident (Y)

Severity Risk Index

628171P 0.50 1.75 0.88

512363H 0.73 1.18 0.86

426309E 0.36 1.78 0.64

755624C 0.84 0.67 0.56

673655X 0.83 0.62 0.51

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6.2.4 List of All Black-Spot s Identified in the Study

As stated in the earlier section, budgetary constraints play a major role in selecting

the safety risk index threshold critical values to decide on the number of crossings

which are the worst ones (black-spots). However, in this study the safety risk index

threshold critical values were set up at 0.15 and with respect to this value a total of

447 black-spots were identified in all four types of protections. They are shown in

Figure 6.14 and summarised in Table 6.6. This total comprises of the numbers of 3,

129, 76 and 239 grade crossings from the Protection Types 1, 2, 3 and 4 respectively.

Identifying Black-Spots Using SRI Threshold Curve - All Protection Types

Severity Risk Threshold CurveX*Y = 0.15

0.00

1.00

2.00

3.00

4.00

5.00

0.00 0.50 1.00 1.50 2.00

Predicted Accidents per Year (X)

Pre

dict

ed E

quiv

alen

t Fat

aliti

es p

er A

ccid

ent (

Y)

447 Crossings (with Severity Risk Value over 0.15) which fall above the Threshold Curve are considered as Black-Spots in All Groups

Grade Crossing (ID No.: 028394Y) at Highest Riskwith Severity Risk Value of 1.20

Figure 6.14: All 447 Black-Spots Identified in Four Protection Types of Grade Crossings

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292

Table 6.6: List of 447 Black-Spots Identified from the Study and Their Locations

Rank

by SRI

Crossing ID

Number

Type of

Protection

Safety Risk

Index Value Crossing Highway City County State

1 028394Y 3 1.20 POPLAR AVE CALIFORNIA KERN CA

2 628171P 4 0.88 HAMMONDVILLE RD. JACKSONVILLE BROWARD FL

3 512363H 4 0.86 LONYO RD NONE WAYNE MI

4 300182S 2 0.77 PUBLIC ROADWAY SOUTHERN

REG.TANGIPAHOA LA

5 794960S 3 0.65 SW 19TH ST REDRIVER DALLAS TX

6 426309E 4 0.64 CR 189 ARKANSAS HEMPSTEAD AR

7 640124J 3 0.59 ATHENS STREET ATLANTA DIVISI BARROW GA

8 755624C 4 0.56 FONDREN ROAD HOUSTON HARRIS TX

9 731968X 2 0.53 GARNER LANE TENNESSEE COLBERT AL

10 352066W 3 0.52 PINEY CHAPEL RD MIDWEST LIMESTONE AL

11 478051H 3 0.52 AIRPORT EXPWAY LAKE ALLEN IN

12 673655X 4 0.51 STATE HIGHWAY 48 SPRINGFIELD CREEK OK

13 725945C 3 0.48 PARIS CRESCENT ST BERNARD LA

14 329012H 2 0.48 MAIN ST. MIDWEST CADDO LA

15 155632M 4 0.46 CO LINE RD CHICAGO LAKE IN

16 718062K 3 0.46 MCDONOUGH BLVD GEORGIA FULTON GA

17 715355D 4 0.46 WEST CRAIGHEAD RO

PIEDMONT MECKLENBURG NC

18 622318S 2 0.46 GLENROSE A TAMPA ORANGE FL

19 715671B 3 0.45 ASCAUGA LAKE RD. PIEDMONT AIKEN SC

20 629688U 4 0.45 TRAINING SCHOOL ROCKY MOUNT NASH NC

21 522595A 4 0.45 TIPTON ST DEARBORN LA PORTE IN

22 014877P 2 0.45 COUNTY ROAD KANSAS LAMB TX

23 732018G 3 0.44 E PORT ST TENNESSEE TISHOMINGO MS

24 483654R 2 0.44 - ILLINO AUDRAIN MO

25 631778T 4 0.43 ELIZABETH AVENUE RALEIGH UNION NC

26 632469J 1 0.43 GODLEY RD FLORENCE

DIVISCHATHAM GA

27 693032T 2 0.43 215TH ST MIDWEST ST CROIX WI

28 525079D 4 0.43 WESTVILLE RD LAKE PREBLE OH

29 437578C 3 0.43 MOUND CITY ARKANSAS CRITTENDEN AR

30 478073H 2 0.42 TR41 LAKE WILLIAMS OH

31 022088L 4 0.42 3RD ST Southeast DALLAS TX

32 300803K 4 0.40 US HWY 49 EAST SOUTHERN

REG. HOLMES MS

33 813642K 2 0.40 CURTIS ST. EASTERN JEFFERSON NE

34 912965D 2 0.39 WEGLEYS RD PITTSBURGH WESTMORELAND PA

35 300653E 3 0.38 MS HWY 32 SOUTHERN REG.

TALLAHATCHIE MS

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Table 6.6: List of 447 Black-Spots Identified from the Study and Their Locations

(Continued)

Rank

by SRI

Crossing ID

Number

Type of

Protection

Safety Risk

Index Value Crossing Highway City County State

36 072894M 3 0.37 MCARTHUR ST CHICAGO MCDONOUGH IL

37 724758R 4 0.36 N STANFORD LANE ILLINOIS JEFFERSON IL

38 538717A 4 0.36 208 CR INDIANAPOLIS LOGAN OH

39 481587S 3 0.36 SR103 LAKE CRAWFORD OH

40 636852M 2 0.36 PELHAM ROAD JACKSONVILLE DECATUR GA

41 304317J 2 0.36 BOLTON ST SOUTHERN REG.

PERRY MS

42 607213R 4 0.35 MUSSER ST. - MUSCATINE IA

43 637253V 2 0.35 CR 351 OAK RIDGE JACKSONVILLE

DPIERCE GA

44 448606J 3 0.35 SH 228B HOUSTON BRAZORIA TX

45 026070P 2 0.35 TURNER ROAD CALIFORNIA SAN BERNARDINO CA

46 082926T 4 0.34 FERRY ST TWIN CITIES ANOKA MN

47 600639M 3 0.34 N. MAIN ST. ARKANSAS

DIVN.ST FRANCIS AR

48 667269Y 3 0.34 CORNERSVILLE RD SPRINGFIELD BENTON MS

49 390642M 2 0.34 BADEN RD SOO LINE DODGE WI

50 352325F 2 0.34 FRANKLIN STREET ATLANTA CHILTON AL

51 513376M 3 0.34 REFUGEE RD DEARBORN FRANKLIN OH

52 027644F 4 0.34 PASSONS BLVD CALIFORNIA LOS ANGELES CA

53 432765T 3 0.33 - DEQUINCY ST LANDRY LA

54 806781N 3 0.33 SR 132 WESTERN JUAB UT

55 522564B 4 0.33 GRANDVIEW AVE DEARBORN ST JOSEPH IN

56 340240U 2 0.33 32ND AVE ATLANTA DIVISI HARRISON MS

57 340252N 2 0.33 FOURNIER AVE ATLANTA DIVISI HARRISON MS

58 435831N 3 0.33 CHARLOTTE DEQUINCY ST LANDRY LA

59 163624R 3 0.32 JOHNSON AVE CHICAGO LAKE IN

60 073281M 2 0.32 N MAXON AVE NEBRASKA ADAMS NE

61 608917D 3 0.32 THROOP ST RID COOK IL

62 300152A 2 0.32 TANGIPAHOA AVE. SOUTHERN

REG.TANGIPAHOA LA

63 155645N 4 0.32 CLARK RD CHICAGO DIVISI LAKE IN

64 348428Y 2 0.32 HOPKINS AVE NASHVILLE DIVI CROCKETT TN

65 522517T 4 0.32 APPLE RD DEARBORN ST JOSEPH IN

66 291194J 3 0.31 US 45 NORTHERN

REG.KANKAKEE IL

67 503541T 4 0.31 STOW RD PITTSBURGH SUMMIT OH

68 167536U 4 0.31 INDIANA ST. CHICAGO KANKAKEE IL

69 175042V 4 0.31 LINCOLN HWY./IL23 CHICAGO DE KALB IL

70 340179T 2 0.31 DORRIES ST ATLANTA DIVISI HARRISON MS

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294

Table 6.6: List of 447 Black-Spots Identified from the Study and Their Locations

(Continued)

Rank

by SRI

Crossing ID

Number

Type of

Protection

Safety Risk

Index Value Crossing Highway City County State

71 025132G 4 0.31 SAN FRANCISCO ST SOUTHWEST COCONINO AZ

72 005129U 2 0.31 5TH ST CHICAGO LINN MO

73 349227L 2 0.30 CAMPER NASHVILLE DIVI DAVIDSON TN

74 605815A 2 0.30 - KANSAS CITY FORD KS

75 503118F 2 0.30 TOWER RD PITTSBURGH ASHTABULA OH

76 831200D 4 0.30 DONOHUE DR ATLANTA DIVISI LEE AL

77 719112P 4 0.30 12TH ST GEORGIA FLOYD GA

78 345951F 4 0.30 CHENOWETH LN LOUISVILLE DIV JEFFERSON KY

79 539242N 4 0.30 RURAL ST GREAT LAKES MARION IN

80 413645B 2 0.30 WHITE STAG XING CENTRAL MCINTOSH OK

81 009598J 4 0.30 CHEYENNE RD KANSAS BUTLER KS

82 253600B 2 0.30 CR 7 (CR 8) DENVER MESA CO

83 624366N 4 0.30 ORIENT RD FLORIDA BUSINE

HILLSBOROUGH FL

84 746784S 4 0.30 BUENA VISTA ST. - LOS ANGELES CA

85 340249F 4 0.30 BROAD STREET ATLANTA DIVISI HARRISON MS

86 294381C 4 0.30 - CHICAGO MACOUPIN IL

87 075356R 2 0.30 MNTH 28 TWIN CITIES STEVENS MN

88 026852D 4 0.30 ROSECRANS AVE WESTERN SAN DIEGO CA

89 728154A 4 0.30 COUNTY ROAD 298 ALABAMA LEE AL

90 390675A 4 0.29 WILLIAMS RD SOO LINE COLUMBIA WI

91 483657L 2 0.29 - ILLINO AUDRAIN MO

92 020046T 2 0.29 EAST PINE LODGE R SOUTHWEST CHAVES NM

93 300207K 4 0.29 PRES. HOOVER ST SOUTHERN

REG.TANGIPAHOA LA

94 017314X 4 0.29 4TH STREET KANSAS HALE TX

95 234824X 3 0.29 HILLTOP RD NONE BERRIEN MI

96 667695G 2 0.29 COUNTY ROAD SPRINGFIELD WRIGHT MO

97 066762N 4 0.29 FEATHER DR NORTHWEST JEFFERSON OR

98 447790V 2 0.29 LAUDERDALE YD RD DEQUINCY ALLEN LA

99 637583B 2 0.28 GILMORE ST JACKSONVILLE

DWARE GA

100 637344B 2 0.28 CASSELS RD WAYCROSS LIBERTY GA

101 525087V 2 0.28 OXFORD-

GETTYSBURG LAKE PREBLE OH

102 062818S 2 0.28 450TH AVE TWIN CITIES OTTER TAIL MN

103 833642P 4 0.28 ROBBERS CREEK NORTHWEST LASSEN CA

104 719983X 3 0.28 MAHER ROAD KENTUCKY BOONE KY

105 768136L 3 0.27 EDDY ST LAFAYETTE CALCASIEU LA

 

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295

Table 6.6: List of 447 Black-Spots Identified from the Study and Their Locations

(Continued)

Rank

by SRI

Crossing ID

Number

Type of

Protection

Safety Risk

Index Value Crossing Highway City County State

106 767687R 3 0.27 LA 88 GULF IBERIA LA

107 628183J 4 0.27 NW 62ND ST. JACKSONVILLE BROWARD FL

108 745997Y 4 0.26 COLDWATER CNYN RD

METROLINK LOS ANGELES CA

109 348089W 3 0.26 CENTER - DICKSON TN

110 746052E 4 0.26 VAN NUYS BLVD - LOS ANGELES CA

111 307690F 2 0.26 RECREATIONAL PARK GULF WOODBURY IA

112 723174U 3 0.26 CENTRAL ST COASTAL COOK GA

113 022694S 1 0.26 HOUSTON ST GULF FORT BEND TX

114 841809U 3 0.26 - KENTUCKY MCCREARY KY

115 592332C 3 0.26 15TH AVENUE HARRISBURG LEBANON PA

116 300186U 2 0.26 BUCKLES LANE SOUTHERN

REG. TANGIPAHOA LA

117 029854C 3 0.25 BROOKSIDE DR CALIFORNIA CONTRA COSTA CA

118 819328W 2 0.25 S CLOVERDALE RD PORTLAND ADA ID

119 009290R 2 0.25 KEELER CONE PLANT KANSAS SEDGWICK KS

120 013796L 4 0.25 ALAMEDA BLVD SOUTHWEST BERNALILLO NM

121 020585G 3 0.25 CHISAM RD TEXAS DENTON TX

122 028582N 4 0.25 PALM AVE CALIFORNIA FRESNO CA

123 272544X 4 0.25 OAKLAND PARK BLVD - BROWARD FL

124 608311K 4 0.25 119TH ST RID COOK IL

125 057190R 4 0.25 96TH AVE COLORADO ADAMS CO

126 481431T 3 0.25 MADISON AVE. LAKE PICKAWAY OH

127 375699B 2 0.25 50E25S NW/C 1-69- - APPANOOSE IA

128 760732J 4 0.25 4TH ST SAN JOAQUIN RIVERSIDE CA

129 028576K 4 0.25 WELDON AVE CALIFORNIA FRESNO CA

130 787736P 3 0.25 PLUM PINE BLUFF OUACHITA AR

131 014592D 2 0.25 RAEF RD KANSAS POTTER TX

132 509478Y 4 0.25 HALLETT AVE DEARBORN FULTON OH

133 012121G 4 0.24 S 29TH STREET TEXAS OKLAHOMA OK

134 500307S 4 0.24 MINER LANE NORTHEAST

CORNEW LONDON CT

135 026519P 4 0.24 MCKINLEY ST CALIFORNIA RIVERSIDE CA

136 507464J 4 0.24 WATER ST. PITTSBURGH ALLEGHENY PA

137 340137G 4 0.24 INDUSTRIAL ROAD ATLANTA DIVISI JACKSON MS

138 545169G 4 0.24 MONROE BLVD NONE WAYNE MI

139 689657J 4 0.24 GRACELAND AVE EASTERN COOK IL

140 272340L 4 0.24 N.E. JENSON BCH.B - MARTIN FL

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Table 6.6: List of 447 Black-Spots Identified from the Study and Their Locations

(Continued)

Rank

by SRI

Crossing ID

Number

Type of

Protection

Safety Risk

Index Value Crossing Highway City County State

141 297477C 4 0.24 CHURCH SOUTHERN

REG.SHELBY TN

142 340180M 2 0.24 HOLLEY ST ATLANTA DIVISI HARRISON MS

143 302426F 2 0.24 MASSEY ST southeast MADISON LA

144 794794C 4 0.24 CR 211 REDRIVER KAUFMAN TX

145 026578S 3 0.24 PLACENTIA AVE CALIFORNIA ORANGE CA

146 789037W 4 0.24 PINE PINE BLUFF MONROE AR

147 638341J 4 0.24 COTTON ST JACKSONVILLE

D DOOLY GA

148 024951U 4 0.23 3RD STREET SOUTHWEST MCKINLEY NM

149 075717T 4 0.23 TH 115 TWIN CITIES MORRISON MN

150 755496W 2 0.23 PRESTON ST EAST TEXAS SHELBY TX

151 600636S 2 0.23 COUNTY RD CR-219 ARKANSAS

DIVN. ST FRANCIS AR

152 745651W 4 0.23 CALIFORNIA ST. LOS ANGELES VENTURA CA

153 628170H 4 0.23 NW 15TH STREET JACKSONVILLE BROWARD FL

154 794533C 4 0.23 PUBLIC FM 3129 REDRIVER CASS TX

155 624820X 4 0.23 FRANK ADAMO DR TAMPA HILLSBOROUGH FL

156 750641B 4 0.23 AVE J SAN JOAQUIN LOS ANGELES CA

157 751198H 4 0.23 CAMELIA ST WESTERN ALAMEDA CA

158 720776A 2 0.23 US 78 FLORENCE DORCHESTER SC

159 841814R 2 0.23 THOMPSON TAPLEY KENTUCKY MCCREARY KY

160 735480V 4 0.23 RUSH STREET PIEDMONT WAKE NC

161 834944V 4 0.23 7TH AVE WESTERN YUBA CA

162 302527S 4 0.23 GOLSON RD southeast OUACHITA LA

163 724578T 3 0.23 46TH/9257N BELT W KENTUCKY ST CLAIR IL

164 012070Y 4 0.23 5TH STREET TEXAS OKLAHOMA OK

165 335092S 2 0.22 LAUREL ST. MIDWEST AVOYELLES LA

166 764311L 4 0.22 BRADY SAN ANTONIO BEXAR TX

167 507059U 4 0.22 NEW MAIN ST. ALBANY DIVISIO ROCKLAND NY

168 732980H 4 0.22 STATE HWY 56 COASTAL RICHMOND GA

169 755901J 4 0.22 KINGPORT ROAD HOUSTON MONTGOMERY TX

170 025651J 4 0.22 GREENWAY RD SOUTHWEST MARICOPA AZ

171 764295E 4 0.22 SOU PRESA SAN ANTONIO BEXAR TX

172 352187U 2 0.22 PHELAN RD/CR 715 MIDWEST CULLMAN AL

173 746484D 4 0.22 MOCKINGBIRD LANE SAN ANTONIO VICTORIA TX

174 532699J 2 0.22 N THAYER RD GREAT LAKE

DIVALLEN OH

175 598394V 4 0.22 SH 101 FT WORTH WISE TX

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Table 6.6: List of 447 Black-Spots Identified from the Study and Their Locations

(Continued)

Rank

by SRI

Crossing ID

Number

Type of

Protection

Safety Risk

Index Value Crossing Highway City County State

176 879162H 2 0.22 CR #950N LAKE HENRY IN

177 413720K 4 0.22 WESLEY ROAD CENTRAL ATOKA OK

178 430112K 4 0.22 CR 202 HOUSTON GRIMES TX

179 794216X 2 0.22 TRUDEAU ST. REDRIVER NATCHITOCHES LA

180 305416K 4 0.22 MAIN ST SOUTHERN

REG.SIMPSON MS

181 388037N 4 0.21 DUNDEE RD MWD COOK IL

182 628191B 4 0.21 OAKLAND PARK BLVD JACKSONVILLE BROWARD FL

183 004398H 2 0.20 TWP RD 60 CHICAGO WILL IL

184 026699P 4 0.20 17TH STREET - ORANGE CA

185 079493L 4 0.20 HARLEM AVE CHICAGO COOK IL

186 531602G 3 0.20 WRANGLE HILL RD HARRISBURG NEW CASTLE DE

187 725656B 3 0.20 ANCHOR LAKE RD CRESCENT PEARL RIVER MS

188 723532B 2 0.20 FLOYD ST. COASTAL LOWNDES GA

189 352121U 2 0.20 E. PINEY GROVE RO MID WEST MORGAN AL

190 284071F 3 0.19 13 MILE RD MIDWEST MACOMB MI

191 023065H 3 0.19 FM 3047 TEXAS MCLENNAN TX

192 638452B 2 0.19 FILMORE ST JACKSONVILLE D

TALBOT GA

193 726719G 2 0.19 BARNES RD ALABAMA CLEBURNE AL

194 345239S 2 0.19 475 SR NASHVILLE DIVI TODD KY

195 058867G 3 0.19 MILL ST NORTHWEST KOOTENAI ID

196 755013M 4 0.19 RENGSTORFF AVE WESTERN SANTA CLARA CA

197 393421V 2 0.18 520TH ST GLENCOE RENVILLE MN

198 026742T 4 0.18 LYON STREET - ORANGE CA

199 750703W 3 0.18 NORTH ST SAN JOAQUIN FRESNO CA

200 372127P 4 0.18 73RD AVE MWD COOK IL

201 386408P 4 0.18 GLENVIEW ROAD MILWAUKEE

NORTCOOK IL

202 757420X 2 0.18 TOWER LINE ROAD SAN JOAQUIN KERN CA

203 253606S 3 0.18 G ROAD & US 6 DENVER MESA CO

204 283602W 4 0.18 LAWRENCE ST/M79 MIDWEST EATON MI

205 062854M 2 0.18 MCHUGH RD TWIN CITIES BECKER MN

206 622828V 3 0.18 GRANGER RD JACKSONVILLE COLUMBIA FL

207 073321H 2 0.18 1600 RD NEBRASKA SALINE NE

208 073280F 2 0.18 S RIVERVIEW AVE NEBRASKA CLAY NE

209 028410F 4 0.18 ARMONA RD CALIFORNIA KINGS CA

210 634990U 2 0.18 WITHERBEE RD. FLORENCE DIVIS

BERKELEY SC

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Table 6.6: List of 447 Black-Spots Identified from the Study and Their Locations

(Continued)

Rank

by SRI

Crossing ID

Number

Type of

Protection

Safety Risk

Index Value Crossing Highway City County State

211 361331H 1 0.18 RARITAN CNTR PKWY EASTERN MIDDLESEX NJ

212 437987U 2 0.18 MABLEY LANE ARKANSAS WHITE AR

213 050468T 3 0.18 GREEN ST ATLANTA DIVISI TROUP GA

214 816915M 2 0.18 - NEBR DAWSON NE

215 634756D 2 0.18 OSPREY RD. FLORENCE ORANGEBURG SC

216 329184R 3 0.18 OXFORD ROAD Texas DE SOTO LA

217 300183Y 2 0.18 PUBLIC ROADWAY SOUTHERN

REG. TANGIPAHOA LA

218 673304Y 3 0.18 O'DELL ST SPRINGFIELD LAWRENCE MO

219 338315R 4 0.18 ELEVENTH ST ALBANY SUFFOLK NY

220 741229C 4 0.18 PENDALE RD TUCSON EL PASO TX

221 639492C 3 0.18 VALLEYWOOD RD ATLANTA FAYETTE GA

222 174009S 4 0.18 NINETEENTH AVENUE SUBURBAN COOK IL

223 079527D 4 0.18 STOUGH ST CHICAGO DU PAGE IL

224 026651M 4 0.18 CERRITOS AVE - ORANGE CA

225 448715M 3 0.18 CR482-RAILROAD AV HOUSTON MATAGORDA TX

226 522533C 4 0.18 MAIN ST DEARBORN ST JOSEPH IN

227 328997A 3 0.18 E ALABAMA AVE MIDWEST CADDO LA

228 746804B 4 0.18 DORAN AVE. - LOS ANGELES CA

229 522562M 4 0.18 OLIVE ST DEARBORN ST JOSEPH IN

230 426602V 2 0.18 HUTTASH HOUSTON CHEROKEE TX

231 745911M 4 0.18 SYCAMORE DRIVE METROLINK VENTURA CA

232 767510Y 2 0.18 ARLINGTON RD GULF ST MARY LA

233 174482H 3 0.17 STATE ST ILLINOIS BOONE IL

234 253564H 3 0.17 CR 263 SO US 6 DENVER GARFIELD CO

235 014343X 2 0.17 CO RD KANSAS WOODS OK

236 831196R 2 0.17 OLD STAGE RD - LEE AL

237 427538C 3 0.17 SH 239 HOUSTON REFUGIO TX

238 689654N 4 0.17 OAKTON BLVD WISCONSIN COOK IL

239 692293P 3 0.17 AURORA RD MIDWEST WASHINGTON WI

240 718025H 3 0.17 PARROTT AVE GEORGIA FULTON GA

241 338164D 4 0.17 COMMACK ROAD ALBANY SUFFOLK NY

242 028585J 4 0.17 WEST AVE CALIFORNIA FRESNO CA

243 152691E 2 0.17 CR #350W LOUISVILLE LAWRENCE IN

244 480068L 2 0.17 - WESTERN MONTGOMERY IL

245 794140U 3 0.17 ULSTER AVE REDRIVER RAPIDES LA

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299

Table 6.6: List of 447 Black-Spots Identified from the Study and Their Locations

(Continued)

Rank

by SRI

Crossing ID

Number

Type of

Protection

Safety Risk

Index Value Crossing Highway City County State

246 174001M 4 0.17 NINTH AVENUE SUBURBAN COOK IL

247 234641E 3 0.17 FRANKLYN 100TH AV CHICAGO DIVISI OTTAWA MI

248 077606H 2 0.17 CO RD COLORADO HITCHCOCK NE

249 511660X 3 0.17 S.HURON RIVER DR. DEARBORN MONROE MI

250 079491X 4 0.17 HOME AVE CHICAGO COOK IL

251 510020U 4 0.17 INDIANA AVE DEARBORN ELKHART IN

252 390658J 2 0.17 SWARTHOUT RD SOO LINE COLUMBIA WI

253 330455R 3 0.17 7TH ST MIDWEST POLK AR

254 029578C 4 0.17 FARMINGTON RD CALIFORNIA SAN JOAQUIN CA

255 226856H 3 0.17 15TH STREET WV BOYD KY

256 026820X 4 0.17 GRAND AVE WESTERN SAN DIEGO CA

257 667346W 3 0.17 PARK ST SPRINGFIELD LEE MS

258 095232C 2 0.17 COUNTY RD NEBRASKA BUCHANAN MO

259 093278J 2 0.17 - TWIN CITIES MCHENRY ND

260 546377L 2 0.17 STUMP GREAT LAKE

DIVCUMBERLAND IL

261 479255X 3 0.17 MOFFIT LANE WESTERN MACON IL

262 028409L 4 0.17 HOUSTON AVE CALIFORNIA KINGS CA

263 155608L 4 0.17 STELLS RD/CR 400E CHICAGO PORTER IN

264 732025S 2 0.17 COUNTY RD 264 TENNESSEE ALCORN MS

265 664073U 2 0.17 CO RD E379 SPRINGFIELD MISSISSIPPI AR

266 438226A 2 0.17 CORD 83 ARKANSAS WHITE AR

267 155626J 4 0.17 HAMSTROM CHICAGO PORTER IN

268 272068N 4 0.17 SOUTH ST - BREVARD FL

269 155490Y 4 0.17 RANGE RD WI LA PORTE IN

270 155391B 4 0.17 7TH ST/FRONT ST CHICAGO KOSCIUSKO IN

271 917020X 4 0.17 GERBER ST DEARBORN NOBLE IN

272 028397U 4 0.17 KIMBERLINA RD CALIFORNIA KERN CA

273 155636P 4 0.17 HOWARD ST CHICAGO LAKE IN

274 391179H 2 0.17 - ST PAUL SERVIC

GOODHUE MN

275 724962P 2 0.17 HIGHWATER RD ILLINOIS FLOYD IN

276 752478N 4 0.17 OLIVE ST. SACRAMENTO STANISLAUS CA

277 025460Y 3 0.17 NORTHERN AVE SOUTHWEST MARICOPA AZ

278 434278D 3 0.17 MOOSE ST CENTRAL CONWAY AR

279 586057V 4 0.17 HENDRICKS AVENUE - CAMDEN NJ

280 057209F 4 0.17 MAIN ST COLORADO WELD CO

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Table 6.6: List of 447 Black-Spots Identified from the Study and Their Locations

(Continued)

Rank

by SRI

Crossing ID

Number

Type of

Protection

Safety Risk

Index Value Crossing Highway City County State

281 176935E 4 0.17 ROHLWING SUBURBAN COOK IL

282 752864Y 4 0.17 "I" ST SACRAMENTO STANISLAUS CA

283 391148J 2 0.17 WINONA ST LA CROSSE WABASHA MN

284 079060F 4 0.17 75E05S NW/C 8-71- NEBRASKA HENRY IA

285 509583A 4 0.17 CR #53 DEARBORN DE KALB IN

286 028459P 4 0.17 AMERICAN AVE CALIFORNIA FRESNO CA

287 622337W 4 0.17 PINE S TAMPA ORANGE FL

288 435812J 3 0.17 POWELL RD DEQUINCY JEFFERSON DAVIS LA

289 346694N 3 0.17 - APPALACHIAN

DI SHELBY KY

290 764232A 2 0.17 CAMINO DELA ROSA SAN ANTONIO EL PASO TX

291 546686Y 4 0.17 BIRCH STREET NORTHEASTER

N PLYMOUTH MA

292 630911S 2 0.16 ELMORE FLORENCE SCOTLAND NC

293 296337W 3 0.16 US HWY 61 - WASHINGTON MS

294 059781B 4 0.16 FAS 224 MONTANA LIBERTY MT

295 303984C 3 0.16 MS HWY 25 southeast MONROE MS

296 637404H 2 0.16 CR 262 JACKSONVILLE

DCLINCH GA

297 515419K 4 0.16 NEW BRIDGE RD PHILADELPHIA BERGEN NJ

298 272492H 4 0.16 ATLANTIC AVE - PALM BEACH FL

299 876689E 2 0.16 TR3 LAKE PUTNAM OH

300 196532V 3 0.16 170TH ST CENTRAL WEBSTER IA

301 794577C 4 0.16 FM1977 EAST TEXAS HARRISON TX

302 028647E 4 0.16 CHILDS AVE CALIFORNIA MERCED CA

303 300164U 4 0.16 FACTORY ST SOUTHERN

REG.TANGIPAHOA LA

304 817621F 4 0.16 N. PINE ST. NEBR HALL NE

305 024950M 4 0.16 2ND STREET SOUTHWEST MCKINLEY NM

306 914663H 2 0.16 HAYES STREET SOUTHEAST RICHLAND LA

307 442398P 2 0.16 CO RD 103 MIDWES SALINE MO

308 517147G 3 0.16 16TH STREET DEARBORN KANAWHA WV

309 340210C 4 0.16 EISENHOWER DR ATLANTA DIVISI HARRISON MS

310 504428D 3 0.16 NORTH ST - WINDHAM CT

311 169870W 3 0.16 - SPRINGFIELD MASON IL

312 426599P 2 0.16 CR 3304 HOUSTON CHEROKEE TX

313 597528N 3 0.16 - EASTERN HOT SPRING AR

314 743688E 4 0.16 CRAVENS ROAD HOUSTON FORT BEND TX

315 518008P 4 0.16 EBY CHIQUES ROAD PHILADELPHIA LANCASTER PA

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Table 6.6: List of 447 Black-Spots Identified from the Study and Their Locations

(Continued)

Rank

by SRI

Crossing ID

Number

Type of

Protection

Safety Risk

Index Value Crossing Highway City County State

316 163578S 4 0.16 CENTRAL FAU2796 CHICAGO DIVISI COOK IL

317 446589N 4 0.16 FM HWY 1660 PALESTINE WILLIAMSON TX

318 517626L 3 0.16 WAGO RD HARRISBURG YORK PA

319 817587B 4 0.16 F AVE. NEBR MERRICK NE

320 746288W 3 0.16 SH 361 HOUSTON SAN PATRICIO TX

321 758519L 4 0.16 BEECHNUT ST HOUSTON HARRIS TX

322 372937G 2 0.16 LEWIS RD/ALL ST - VIGO IN

323 732125W 4 0.16 BYHALIA RD TENNESSEE SHELBY TN

324 302523P 2 0.16 CHENIERE STATION southeast OUACHITA LA

325 028403V 4 0.16 JACKSON AVE CALIFORNIA KINGS CA

326 155274F 2 0.16 PLUM STREET LOUISVILLE DIV AUGLAIZE OH

327 028714W 4 0.16 EL CAPITAN WAY CALIFORNIA MERCED CA

328 478273S 4 0.16 JEFFERSON ST LAKE HUNTINGTON IN

329 026516U 4 0.16 BUCHANAN ST CALIFORNIA RIVERSIDE CA

330 272073K 4 0.16 COQUINA AVE - BREVARD FL

331 741815W 4 0.16 GUADALUPE RD WEST COLTON MARICOPA AZ

332 349329E 2 0.16 - - RUTHERFORD TN

333 538921Y 4 0.16 CR 100S GREAT LAKES MADISON IN

334 329305L 2 0.16 AMBLER ROAD Texas VERNON LA

335 724641H 2 0.16 - KENTUCKY CLINTON IL

336 751291P 4 0.16 CANNON RD WESTERN SOLANO CA

337 081018G 4 0.16 WASHINGTON AVE TWIN CITIES BECKER MN

338 469382W 4 0.16 UNION ST VIRGINIA SALEM VA

339 053049F 4 0.16 SUTTON STREET MBTA ESSEX MA

340 349326J 4 0.16 W MAIN ST - RUTHERFORD TN

341 787543R 2 0.16 CASTLEBERRY PINE BLUFF CLAY AR

342 329181V 2 0.16 PEGUES ST Texas DE SOTO LA

343 179945V 4 0.16 APPLETON @

PACKARMIDWEST OUTAGAMIE WI

344 004475F 4 0.16 E 20TH RD CHICAGO LA SALLE IL

345 638228R 2 0.16 - JACKSONVILLE

D COFFEE GA

346 086580G 2 0.16 - TWIN CITIES GRAND FORKS ND

347 020566C 2 0.16 TN SKILES RD TEXAS DENTON TX

348 752487M 4 0.16 FULKERTH RD SACRAMENTO STANISLAUS CA

349 069965D 4 0.16 IOWA ST CHICAGO CRAWFORD WI

350 745998F 4 0.16 BELLAIRE AVE METROLINK LOS ANGELES CA

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Table 6.6: List of 447 Black-Spots Identified from the Study and Their Locations

(Continued)

Rank

by SRI

Crossing ID

Number

Type of

Protection

Safety Risk

Index Value Crossing Highway City County State

351 272465L 4 0.16 6TH AVE S. - PALM BEACH FL

352 538976L 4 0.16 REFORMATORY RD GREAT LAKES MADISON IN

353 026863R 4 0.16 LAUREL ST WESTERN SAN DIEGO CA

354 176809K 4 0.16 YORKHOUSE RD WISCONSIN LAKE IL

355 193422A 2 0.16 THOMPSON RAVINE R EASTERN BLUE EARTH MN

356 833920D 4 0.16 LATHROP RD WESTERN SAN JOAQUIN CA

357 478618K 4 0.16 US #421 LAKE LA PORTE IN

358 673662H 2 0.16 COUNTY ROAD SPRINGFIELD CREEK OK

359 720017R 2 0.16 LOCUST ST KENTUCKY BOONE KY

360 190533G 2 0.16 OLD BRIDGE RD CENTRAL LINN IA

361 756532T 4 0.16 IRVING RD 3268 OREGON LANE OR

362 735236Y 4 0.16 ELLIS RD EASTERN DURHAM NC

363 794832J 4 0.16 SAM HOUSTON RD RIO GRANDE DALLAS TX

364 841751N 2 0.16 - KENTUCKY PULASKI KY

365 521142E 4 0.16 WINTON RD ALBANY MONROE NY

366 605533J 4 0.16 - KANSAS CITY SEWARD KS

367 190721W 4 0.16 S AVE CENTRAL BOONE IA

368 335043V 2 0.16 ED GREMILLION RD MIDWEST AVOYELLES LA

369 789084E 4 0.16 - MIDWES STODDARD MO

370 331585R 2 0.16 RD 2417 SOUTHEAST HOPKINS TX

371 759664N 4 0.16 MARKET ST OREGON MARION OR

372 628165L 4 0.16 PALMETTO PARK RD JACKSONVILLE PALM BEACH FL

373 434062X 2 0.16 CO RD CENTRAL WAGONER OK

374 517780J 2 0.16 BROAD - LUZERNE PA

375 303966E 2 0.16 SECTION RD southeast CLAY MS

376 300570R 4 0.16 ASKEW RD SOUTHERN

REG. PANOLA MS

377 300847K 4 0.16 CROSSOVER RD SOUTHERN REG.

YAZOO MS

378 437558R 2 0.16 BINGS STORE RD. ARKANSAS CRITTENDEN AR

379 719093M 4 0.16 CR 173 GEORGIA FLOYD GA

380 750511E 4 0.16 YUBA ST SACRAMENTO SHASTA CA

381 342274V 4 0.16 POPLAR ST CHICAGO VIGO IN

382 082479U 4 0.15 MAIN ST TWIN CITIES CHIPPEWA MN

383 020597B 2 0.15 COUNTY ROAD TEXAS COOKE TX

384 155065X 4 0.15 MIAMI CHAPEL RD DETROIT MONTGOMERY OH

385 744846F 4 0.15 LAMAR ST. SAN ANTONIO ROBERTSON TX

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Table 6.6: List of 447 Black-Spots Identified from the Study and Their Locations

(Continued)

Rank

by SRI

Crossing ID

Number

Type of

Protection

Safety Risk

Index Value Crossing Highway City County State

386 302582S 4 0.15 S. MAPLE ST. southeast BIENVILLE LA

387 069947F 4 0.15 CO PARK ACCESS RD CHICAGO GRANT WI

388 794261S 2 0.15 PARISH RD 601 REDRIVER RED RIVER LA

389 692566G 4 0.15 - WISCONSIN PORTAGE WI

390 722324W 4 0.15 RANDOLPH ST PIEDMONT DAVIDSON NC

391 731786L 4 0.15 Moon Town Road TENNESSEE MADISON AL

392 288983E 4 0.15 2100 N NORTHERN

REG. IROQUOIS IL

393 081737T 2 0.15 CSAH 7 TWIN CITIES CLEARWATER MN

394 795328A 4 0.15 BONNIE BREA FT WORTH DENTON TX

395 274633W 4 0.15 COUNTY ROAD TEXAS WISE TX

396 673738L 4 0.15 US HIGHWAY SPRINGFIELD NOBLE OK

397 507701T 4 0.15 AMITY ST PITTSBURGH ALLEGHENY PA

398 427961P 4 0.15 HERRING AVE PALESTINE MEDINA TX

399 664102C 4 0.15 CHESTNUT EXPWY SPRINGFIELD GREENE MO

400 480084V 4 0.15 TIMBER RD ILLINOIS MACOUPIN IL

401 441427U 4 0.15 NIPECKELS RR HOUSTON MOREHOUSE LA

402 335374H 4 0.15 ROBERT E LEE MIDWEST BOSSIER LA

403 353422T 4 0.15 PLEASANT ST APPALACHIAN

DI HARRISON KY

404 815131G 2 0.15 - EASTERN TREGO KS

405 415992E 4 0.15 SPARKS CENTRAL JOHNSON TX

406 441320S 4 0.15 *PUBLIC LA059 HOUSTON OUACHITA LA

407 193105V 2 0.15 OGAN AVE CENTRAL POWESHIEK IA

408 634680A 4 0.15 STATE ST SAVANNAH LEXINGTON SC

409 415729D 2 0.15 CR 166/TRACK RD SAN ANTONIO CALDWELL TX

410 725837F 4 0.15 20TH STREET NE CRESCENT DE KALB AL

411 483697J 4 0.15 COATES STREET ILLINO RANDOLPH MO

412 413891L 2 0.15 MARTIN L. KING ST NORTHERN OKLAHOMA OK

413 070832H 4 0.15 4TH STREET N TWIN CITIES CASS ND

414 067927M 4 0.15 14TH ST TWIN CITIES SWIFT MN

415 665261M 2 0.15 FREEMANVILLE RD MEMPHIS ESCAMBIA AL

416 019733C 2 0.15 SNOW RD SOUTHWEST DONA ANA NM

417 762301Y 4 0.15 BRECKENRIDGE ST SACRAMENTO TEHAMA CA

418 290535W 4 0.15 LIVINGSTON ROAD CHICAGO LIVINGSTON IL

419 012033W 4 0.15 BEEMER RD TEXAS LOGAN OK

420 352177N 4 0.15 9TH ST SW MIDWEST CULLMAN AL

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Table 6.6: List of 447 Black-Spots Identified from the Study and Their Locations

(Continued)

Rank

by SRI

Crossing ID

Number

Type of

Protection

Safety Risk

Index Value Crossing Highway City County State

421 725148L 4 0.15 SPIEHLER RD. CRESCENT ST TAMMANY LA

422 349378B 4 0.15 NORMANDY ROAD NASHVILLE DIVI BEDFORD TN

423 305433B 2 0.15 MYERS RD SOUTHERN REG.

RANKIN MS

424 522778T 4 0.15 RIPLEY\US6\SR51 CHICAGO LAKE IN

425 303299K 4 0.15 LA 441 SOUTHERN

REG.LIVINGSTON LA

426 011722M 4 0.15 NS-297 SPRINGFIELD GARFIELD OK

427 362864W 4 0.15 NEW MARKET AVE PHILADELPHIA MIDDLESEX NJ

428 272422T 4 0.15 CLEMATIS ST. - PALM BEACH FL

429 796358V 4 0.15 ST JOSEPH RIOGRANDE MARTIN TX

430 725816M 4 0.15 SCHOOL STREET CRESCENT DE KALB AL

431 586053T 4 0.15 ATCO AVENUE - CAMDEN NJ

432 155052W 4 0.15 LOWER MIAMISBURG DETROIT MONTGOMERY OH

433 263412N 4 0.15 MIDLAND AVE 93 BERGEN NJ

434 447709F 2 0.15 PELICAN HWY. DEQUINCY ALLEN LA

435 229448H 4 0.15 THORNTON ST LOUISVILLE DIV CAMPBELL KY

436 163638Y 4 0.15 KENNEDY CHICAGO DIVISI LAKE IN

437 597738D 4 0.15 ROCK ISLAND RD TEXAS DALLAS TX

438 751699M 4 0.15 - WESTERN CONTRA COSTA CA

439 258231Y 2 0.15 DIXON RD. MIDWEST MONROE MI

440 595485R 4 0.15 DUTOON RD - GRADY OK

441 513656P 2 0.15 E MAIN ST CENTRAL(SOUTH)

WOOD OH

442 789790P 4 0.15 CR 1330 EAST TEXAS CAMP TX

443 012056D 4 0.15 SIMPSON ROAD TEXAS LOGAN OK

444 668433D 4 0.15 CO RD SPRINGFIELD OTTAWA OK

445 448476P 4 0.15 BOECHER RD SAN ANTONIO FRIO TX

446 513626X 4 0.15 AMON ST. DETROIT DIVISI WOOD OH

447 434135F 4 0.15 SHIRLEY RD WICHITA SEQUOYAH OK

An analysis on these black-spots shows that all of the 447 black-spots are found

within 39 individual states in USA. Table 6.7 shows the top 10 states in which the

higher number of black-spots has been identified. The state of California has the

highest number of black-spots (47) followed by Texas (44), Louisiana (35), Illinois

(33) and so on. In total, there are 274 individual counties contain these 447 black-

spots. Table 6.8 illustrates the top 8 counties in which the higher number of black-

spots has been identified. The county of Cook has the highest number of black-spots

(13) followed by Los Angeles (7) and so on.

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Table 6.7: Number of Black-Spots Identified by Top Ten States

State Total Number of Black-spots Identified

California (CA) 47

Texas (TX) 44

Louisiana (LA) 35

Illinois (IL) 33

Indiana (IN) 29

Mississippi (MS) 22

Georgia (GA) 19

Florida (FL) 17

Ohio (OH) 17

Oklahoma (OK) 16

Table 6.8: Number of Black-Spots Identified by Top Eight Counties

County State Total Number of Black-spots Identified

COOK Illinois (IL) 13

LOS ANGELES California (CA) 7

HARRISON Mississippi (MS) 6

LAKE Indiana (IN) 6

TANGIPAHOA Louisiana (LA) 6

BROWARD Florida (FL) 5

FRESNO California (CA) 5

ORANGE California (CA) 4

6.2.5 Validation of Safety Risk Index (SRI) Model

A comparison technique is utilised to validate (using goodness-of-fit) the Safety Risk

Index model developed in this study. Basically, it compares the relationship between

the top 447 crossings individually identified from the SRI method and from the

ranking methods by highest accidents and consequences in the history. Figure 6.15

depicts three circles (Circle-A, Circle-B and Circle-C) represent:

• Circle-A: All 447 black-spots identified by safety risk index method;

• Circle-B: Top 447 crossings ranked by highest number of accidents

historically (2001-2005); and

• Circle-C: Top 447 crossings ranked by highest accidental consequences

historically (2001-2005).

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17

60

115

Circle-C: Top 447 Crossings Ranked by Highest Accidental Consequences

in History (2001-2005)

Circle-B: Top 447 Crossings Ranked by Highest Number of

Accidents in History (2001-2005)

Circle-A: 447 Black-spots Crossings Identified by

Safety Risk Index Method

Figure 6.15: Graphical Demonstration on Comparison of Black-Spots to the Crossings

Ranked by Highest Number of Accidents and Highest Consequences historically

Table 6.9: Common 17 Black-Spots Identified in All Three Circles (A, B and C)

Crossing ID Number

SRI Value Estimated from Models

Number of Accidents in History (2001-2005)

Number of Equivalent Fatalities in History (2001-2005)

731968X 0.53 2 3

637253V 0.35 2 2

075356R 0.30 2 2

020046T 0.29 4 1

062818S 0.28 3 1

819328W 0.25 2 1

720776A 0.23 3 1

352187U 0.22 2 1

638452B 0.19 2 1

831196R 0.17 2 1

152691E 0.17 2 1

724962P 0.17 2 1

391148J 0.17 2 1

637404H 0.16 2 1

372937G 0.16 2 1

193422A 0.16 2 1

193105V 0.15 2 1

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In comparing Circle-A and Circle-B, it was noted that 17 grade crossings (3.8%)

from the top 447 crossings ranked by highest accidents historically (2000-2005) are

included in the group of black-spots identified in this study. Similarly, by comparing

Circle-A and Circle-C, 132 crossings (29.5%) from the top 447 crossings ranked by

highest consequences historically are the same in the group of black-spots. However,

overall 17 grade crossings (3.8%) are commonly found in all three circles and are

shown in Table 6.9.

This analysis results shows that:

• The safety risk index model developed in the study to identify black-spots

seems to be in good shape, reasonably fitting to the historical black-spots

ranked by highest number of accidents and consequences at crossings; and

• The criteria, to identify the black-spots, heavily depends on the ranking of

highest consequences rather than highest number of accidents at crossings

historically.

6.2.6 Analysis of Black-spot Cluster Regions (All Protection

Types)

In the previous section, a total of 447 black-spots are identified individually with

respect to the severity risk index threshold critical values set up at 0.15 in all four

types of protections. These black-spots from all protection types are now grouped

together and plotted in Figure 6.16 for a further study called “cluster region

analysis”. As shown in the Figure, three types of cluster regions (Regions A, B and

C) are identified as follows:

• Region-A represents the group of black-spots with low frequency of

accidents and high consequences;

• Region-B identifies the group of black-spots with moderate frequency of

accidents and moderate consequences; and

• Region-C recognises the group of black-spots with high frequency of

accidents and low consequences.

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Analysing Cluster Regions Identified within 447 Black-Spots

Severity Risk Threshold Curve X*Y = 0.15

0.00

1.00

2.00

3.00

4.00

5.00

0.00 0.50 1.00

Predicted Accidents per Year (X)

Pre

dict

ed E

quiv

alen

t Fat

aliti

es p

er A

ccid

ent (

Y)

Cluster Region-A Black-spots

Cluster Region-B Black-spots

Cluster Region-C Black-spots

Exceptional Black-spot ID No: 028394Y

AP

BP

CP

Figure 6.16: Three Cluster Regions of 447 Black-Spots in All Protection Types

The crossings, which are estimated with same safety risk index values, may be

spatially dispersed anywhere over Regions A, B, and C. For example, consider three

crossings, which are represented at the points of AP , BP and CP on the threshold

curve as indicated in the Figure. Even though the safety risk index for all three

crossings is assigned to have the same value of 0.15, they fall in the Regions A, B,

and C respectively. AlthoughAP , BP and CP indicate three crossings with the same

safety status, they have the risk nature of low accidents-high consequences,

moderate accidents-moderate consequences and high accidents-low consequences

respectively. Different types of intervention strategies are therefore required to

enhance the safety at these three crossings even though the risk index value is the

same for all. This means crossing AP is in urgent need of a safety intervention

program to minimise its consequences risk. A safety intervention program to reduce

accident risk is urgently needed for crossingCP . For crossingBP , there is a moderate

need for both programs to be implemented to reduce the risks of accidents and

consequences. For the exceptional black-spot case such as crossing ID Number:

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028394Y (which does not fall under any of the cluster regions specified), both

programs are urgently needed to minimise the risks of accidents and consequences.

The reason for this analysis is to identify appropriate types of strategies according to

specific safety issues at each grade crossing. However, the counter-measures applied

to minimise accidental consequences need to vary from the counter-measures

tailored to reduce frequency of accidents.

6.3 Summary

In this chapter, A Safety Risk Index (a quantitative measure) to assess and prioritise

safety risks at railway grade crossings is introduced, described and developed. It is

illustrated using a set of data drawn from a source of data set covering large rail

infrastructure. The model is developed, using appropriate variables and factors that

are used to initially develop models for predicting accidents and consequences. The

Safety Risk Index (SRI) model, developed using individual models of prediction of

accidents and consequences is illustrated using estimation of scores at each grade

crossing and graphical representation of scores over key variables. Combined scores

and graphical representation of scores over key variables are used to assess the safety

risk at each rail crossing. Further, they are used to identify black-spots. Using those

scores and graphical representation of scores over key variables, it is noted that there

are 447 black-spot grade crossings across the entire rail infrastructure considered.

Various aspects of those black-spots and scores are described and summarised.

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Chapter 7

Impact Analysis on Risk Assessment Models

7.0 Introduction

The approaches used in the development of safety risk assessment models for

assessing and prioritising safety risks at railway grade crossings were introduced

and presented in previous chapters (chapter 5 and 6). Further, the final risk

assessment model (Safety Risk Index), developed using individual models of

prediction of accidents and consequences was illustrated using estimation of scores

at each grade crossing and graphical representation of scores over key variables.

These three models (Accidents prediction, Consequence prediction and Severity risk

index models) are represented by relevant mathematical formulations, involving a

number of significant variables selected through appropriate selection methods.

Since these models are developed and tested using a static data set, prediction of

accidents, consequences and safety risk at rail crossings across a range of selected

variables can easily be visualised using the model sensitivity. In order to investigate

the model sensitivity across these variables, an impact analysis of risk factors

(sensitivity analysis) is proposed and carried out as part of this research. Therefore,

this chapter presents details of impact analysis of risk factors.

This chapter first describes a detailed sensitivity analysis which studies variables

that have had a significant impact on collisions and consequences at public grade

crossings. All three types of models generated in this study are examined and their

results of impact analysis are discussed in the summary.

7.1 Impact (Sensitivity) Analysis

Impact or sensitivity analysis of a model can help analysts to determine relative

effects of associated model parameters on model results. The impact analysis will

extend the preliminary analysis by identifying which parameters are important to the

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prediction of imprecision - how sensitive the parameters are to change the values and

the structure of a predictive model. Akgungor and Yildiz (2007, p.64) stated that the

most common sensitivity method used worldwide is the traditional “Change one

factor at a time” approach. Using the same approach in this study, the impact

analysis is conducted to identify and study the impact of characteristics that influence

risks at grade crossings. Figure 7.1 shows the flow diagram for impact analysis on

three risk assessment models generated in this study. The type of relationship

between the risk indicators (such as accident frequency and accidental consequences)

and the parameters within risk factor groups (such as railway and highway

characteristics) is identified and examined using the risk assessment models

equations given in previous chapters. The analysis is initially performed for a

particular type of protection at crossings through estimating the value of the risk

indicator, by changing the value of a particular parameter at a time, while controlling

other parameters at fixed values. This procedure is repeated for other types of

protection and the relationships are examined by depicting relevant risk indicator

curves on same graphs. The summary on findings is finally discussed.

Impact Analysis on Models• Accident Frequency • Accidental Consequences • Safety Risk Index

Highway Characteristics• Annual Average Daily Traffic • Highway Speed • Number of Traffic Lanes

Railway Characteristics• Daily Train Traffic • Train Speed • Number of Tracks

Protection Types• No Signs or No Signals • Stop Signs or Cross-bucks • Signals, Bells or Warning Devices • Gates or Full Barrier

Figure 7.1: Flow Diagram for Impact Analysis on Models Developed in the Study

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Two considerations were taken into account to conduct the impact analysis. Firstly,

there were three models (Poisson, Negative Binomial and Empirical Bayesian)

initially developed and checked for their goodness-of-fit to predict accidents

frequency and consequences. The Empirical Bayesian model (adjusted to the NB

model) was the best prediction fit for all types of protection as shown in the earlier

chapter. However, the EB model was considered to be too complex to perform the

impact analysis on the frequency of accidents, as it requires the accident history of

each location, so the NB model was selected for its suitability for the impact analysis

in this chapter. Secondly, three types of upgrading (A, B and C as explained below)

on crossings were considered in this analysis between the crossings equipped with

Protection type 1 (No signs or no signals), Protection type 2 (Stop signs or cross-

bucks), Protection type 3 (Signals, bells or warning devices) and Protection type 4

(Gates or full barrier) as follows:

• Upgrading-A: From Protection type 1 to Protection type 2;

• Upgrading-B: From Protection type 2 to Protection type 3; and

• Upgrading-C: From Protection type 3 to Protection type 4.

7.2 Examining Models Predicting Collisions

When examination of sensitivity is carried out on model predicting collisions by its

constructed parameters individually, only one of the parameters is considered as

variable and the others are controlled by given values. In this study, the controlled

value for each parameter is selected as the approximate mean value of relevant

parameters for all crossing types. The groups of risk factors and the controlled values

of parameters in modelling are shown in Table 7.1.

Table 7.1: Controlled Values for Parameters Constructing Collisions Prediction Models

Characteristic Parameter of Models Controlled Value

Highway

Annual Average Daily Traffic 5000 vehicles

Highway Speed 35 mph

Number of Traffic Lanes 2

Railway

Daily Train Traffic 20 trains

Maximum Timetabled Train Speed 50 mph

Number of Main Tracks 1

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7.2.1 Effects of Highway Characte ristics on Four Protection Types

In the models predicting collisions, there were three parameters related to highway

characteristics identified (Annual average daily traffic, Number of traffic lanes and

Highway speed). Sensitivity of models predicting collisions by these three

parameters is examined below.

Annual Average Daily Traffic (AADT) Figure 7.2 depicts the relationship between the predicted collisions per year versus

Annual average daily traffic for the four types of protection. The predicted collisions

at grade crossings increase as AADT increases. This implies that highway traffic

volume has a negative effect on the safety of grade crossings regardless of the type of

protection. However, the rate of collision depends on the type of protection equipped

at crossings.

Annual Predicted Collision Vs Annual Average Daily Traffic

0.00

0.20

0.40

0.60

0.80

1.00

1,000 5,00010,000

20,00040,000

120,000300,000

Annual Average Daily Traffic

Pre

dict

ed C

ollis

ion

Crossings w ith No Stop Signs (P1) Crossings w ith Stop Signs (P2)

Crossings w ith Flashing Lights (P3) Crossings w ith Gates (P4)

Figure 7.2: Effect of Annual Average Daily Traffic on Annual Collision Prediction by

Protection Type (Controlled by Daily Train Traffic = 20 trains; Maximum Timetabled Train

Speed = 50 mph; Highway Speed = 35 mph; Number of Traffic Lanes = 2; and Number of

Main Tracks = 1)

Grade crossings without any stop signs or signals have the highest rate of increase

followed by crossings with stop signs; crossings with flashing lights; and crossings

with gates. This means that highway traffic volume has an exceptionally higher

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effect on collisions occurring at no-stop sign grade crossings than those at crossings

with signs, flashing lights and gates.

Number of Traffic Lanes The relationship between the predicted collisions per year versus Number of traffic

lanes for the four types of protection is depicted in Figure 7.3. It shows that the

number of traffic lanes has no effect on the occurrence of collisions at no-stop sign

crossings and has a slight positive effect at crossings with flashing lights or gates.

However, the predicted collisions at crossings with stop signs considerably increase

with increasing numbers of traffic lanes. It is noted that, regardless of the number of

traffic lanes, more collisions are expected at no-stop sign crossings (about five times

higher) compared with the other types of crossings for the same controlled value of

other parameters.

Annual Predicted Collision Vs Number of Traffic Lanes

0.000.100.200.300.400.500.60

1 2 4 6 8 10

Number of Traffic Lanes

Pre

dict

ed C

ollis

ion

Crossings w ith No Stop Signs (P1) Crossings w ith Stop Signs (P2)

Crossings w ith Flashing Lights (P3) Crossings w ith Gates (P4)

Figure 7.3: Effect of Number of Traffic Lanes on Annual Collision Prediction by

Protection Type (Controlled by Annual Average Daily Traffic = 5000 vehicles; Daily Train

Traffic = 20 trains; Maximum Timetabled Train Speed = 50 mph; Highway Speed = 35

mph; and Number of Main Tracks = 1)

Highway Speed Figure 7.4 illustrates the relationship between the predicted collisions per year versus

Highway speed (mph) for the four types of protection. It shows that highway speed

has no effect on the occurrence of collisions at no-stop sign and gate crossings and

has a negligible effect at crossings with signs and flashing lights. It is noted that,

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315

regardless of highway speed, more collisions are expected at stop sign crossings

(about two times higher) compared with crossings with flashing lights or gates for

the same controlled value of other parameters. The predicted collisions at no-stop

sign crossings are about four times higher than crossings with stop signs.

Annual Predicted Collision Vs Highway Speed

0.000.100.200.300.400.500.60

15 30 45 60 75

Highway Speed

Pre

dict

ed C

ollis

ion

Crossings w ith No Stop Signs (P1) Crossings w ith Stop Signs (P2)

Crossings w ith Flashing Lights (P3) Crossings w ith Gates (P4)

Figure 7.4: Effect of Highway Speed on Annual Collision Prediction by Protection Type

(Controlled by Annual Average Daily Traffic = 5000 vehicles; Daily Train Traffic = 20

trains; Maximum Timetabled Train Speed = 50 mph; Number of Traffic Lanes = 2; and

Number of Main Tracks = 1)

7.2.2 Effects of Railway Character istics on Four Protection Types

There were three parameters related to railway characteristics identified (Daily train

movement, Number of main tracks and Train Speed) in the models predicting

collisions. Sensitivity of models predicting collisions by these three parameters is

examined below.

Daily Train Traffic Figure 7.5 depicts the relationship between the predicted collisions per year versus

Daily train traffic for the four types of protection. The predicted collisions at grade

crossings increased as train traffic increased for all grade crossings except no-stop

sign crossings. This implies that train traffic volume has a negative effect on the

safety of grade crossings other than no-stop sign types. However, the rate of collision

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increase depends on the type of protection equipped at crossings. Grade crossings

with stop signs or signals have the highest rate of increase followed by crossings

with flashing lights, and then crossings with gates. This means that train traffic

volume has an exceptionally higher effect on collisions occurring at stop signs or

signals grade crossings than those at crossings with flashing lights and gates. It is

noted that train traffic volume has no effect on the occurrence of collisions at no-stop

sign crossings. One possible explanation for this result is that the majority of no-stop

sign crossings have less volume of train traffic.

 

Annual Predicted Collision Vs Daily Train Traffic

0.000.100.200.300.400.500.60

10 50 100 150 200

Daily Train Traffic

Pre

dict

ed C

ollis

ion

Crossings w ith No Stop Signs (P1) Crossings w ith Stop Signs (P2)

Crossings w ith Flashing Lights (P3) Crossings w ith Gates (P4)

Figure 7.5: Effect of Daily Train Traffic on Annual Collision Prediction by Protection

Type (Controlled by Annual Average Daily Traffic = 5000 vehicles; Maximum Timetabled

Train Speed = 50 mph; Highway Speed = 35 mph; Number of Traffic Lanes = 2; and

Number of Main Tracks = 1)

Number of Main Tracks The relationship between the predicted collisions per year versus Number of main

tracks for the four types of protection is depicted in Figure 7.6. It shows that the

number of main tracks has no effect on the occurrence of collisions at any crossings

other than gate types, which showed little effect. It is noted that more collisions at

no-stop sign crossings are expected regardless of main tracks than at other types of

crossings for the same controlled value of other parameters.

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Annual Predicted Collision Vs Number of Main Tracks

0.000.100.200.300.400.500.60

1 2 3 4 5 6 7

Number of Main Tracks

Pre

dict

ed C

ollis

ion

Crossings w ith No Stop Signs (P1) Crossings w ith Stop Signs (P2)

Crossings w ith Flashing Lights (P3) Crossings w ith Gates (P4)

Figure 7.6: Effect of Number of Main Tracks on Annual Collision Prediction by

Protection Type (Controlled by Annual Average Daily Traffic = 5000 vehicles; Daily Train

Traffic = 20 trains; Maximum Timetabled Train Speed = 50 mph; Highway Speed = 35

mph; and Number of Traffic Lanes = 2)

Train Speed Figure 7.7 illustrates the relationship between the predicted collisions per year versus

Train speed (mph) for the four types of protection. It is noted that train speed has no

effect on the occurrence of collisions at crossings with gates, and medium effect on

crossings with no-stop signs. Other types of crossings have little effect. It can be seen

that more collisions at no-stop sign crossings are expected, regardless of train speed,

than at other types of crossings for the same controlled value of other parameters.

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Annual Predicted Collision Vs Maximum Train Timetabled Speed

0.00

0.05

0.10

0.15

0.20

20 40 60 80 100

Maximum Train Timetabled Speed

Pre

dict

ed C

ollis

ion

Crossings w ith No Stop Signs (P1) Crossings w ith Stop Signs (P2)

Crossings w ith Flashing Lights (P3) Crossings w ith Gates (P4)

Figure 7.7: Effect of Maximum Timetabled Train Speed on Annual Collision Prediction

by Protection Type (Controlled by Annual Average Daily Traffic = 5000 vehicles; Daily

Train Traffic = 20 trains; Highway Speed = 35 mph; Number of Traffic Lanes = 2; Number

of Main Tracks = 1)

7.2.3 Effects of Upgrading Protec tion Types on Co llisions Related

to Highway Characteristics

As indicated earlier, three types of upgrading (Upgrading-A: From Protection type 1

to Protection type 2; Upgrading-B: From Protection type 2 to Protection type 3; and

Upgrading-C: From Protection type 3 to Protection type 4) on crossings were

considered in this analysis between crossings equipped with four protection types.

Sensitivity of models predicting collision ratios related to the three highway

parameters (Annual average daily traffic, Number of traffic lanes and Highway

speed) by these three upgrading types is examined below.

Annual Average Daily Traffic (AADT) Figure 7.8 depicts the ratios of predicted collisions among the four types of

protection types as related to Annual Average Daily Traffic. Three observations have

emerged from this sensitivity analysis. The first observation is that the ratios of

expected collisions for all upgrading are consistently lower than the value of 1.0 for

all available range of AADT. This suggests that if crossings are upgraded from ‘No-

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stop signs’ to ‘Stop signs’; or from ‘Stop signs’ to ‘Flashing lights’; or from

‘Flashing lights’ to ‘Gates’, some reduction in the number of collisions would occur

irrespective of the volume of highway traffic. Secondly, the model suggests that

while it is always beneficial to upgrade crossings, AADT graphically shows a slight

positive impact on the benefit for the types of Upgrading - B and Upgrading - C.

Thirdly, the type of upgrading shows a large reduction in collisions over the high

range of AADT (around 20,000). This indicates that if crossings are upgraded from

‘No-stop signs’ to ‘Stop signs’, it is expected there would be more than three times

the reduction in the number of collisions at high range of the volume of highway

traffic.

Ratio of Predicted Collision Vs Annual Average Daily Traffic

0.000.200.400.600.801.00

1,00010,000

20,00040,000

60,00080,000

100,000

Annual Average Daily Traffic

Rat

io o

f Pre

dict

ed

Col

lisio

n

Upgrading-A (P2 / P1): Crossings w ith Stop Signs / Crossings w ith No Stop Signs

Upgrading-B (P3 / P2): Crossings w ith Flashing Lights / Crossings w ith Stop Signs

Upgrading-C (P4 / P3): Crossings w ith Gates / Crossings w ith Flashing Lights

Figure 7.8: Effect of Annual Average Daily Traffic on Predicted Collision Ratio when

Comparing Two Protection Types (Controlled by Daily Train Traffic = 20 trains;

Maximum Timetabled Train Speed = 50 mph; Highway Speed = 35 mph; Number of Traffic

Lanes = 2; and Number of Main Tracks = 1)

Number of Traffic Lanes Figure 7.9 shows the ratios of predicted collisions among the four types of protection

types as related to number of traffic lanes. Three observations have emerged from

this sensitivity analysis. The first observation is that the ratios of expected collisions

for all upgrading are consistently lower than the value of 1.0 for all available range

of number of traffic lanes. This suggests that if crossings are upgraded from ‘No-stop

signs’ to ‘Stop signs’; or from ‘Stop signs’ to ‘Flashing lights’; or from ‘Flashing

lights’ to ‘Gates’, some reduction in the number of collisions would occur

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irrespective of the number of traffic lanes. Secondly, the number of traffic lanes has a

slight positive impact on the benefit for all types other than Upgrading - A. Thirdly,

it is noted that more collisions reduction for Upgrading - A are expected regardless

of the number of traffic lanes than at other types of crossings for the same controlled

value of other parameters.

Ratio of Predicted Collision Vs Number of Traffic Lanes

0.000.200.400.600.801.00

1 2 4 6 8

Number of Traffic Lanes

Rat

io o

f Pre

dict

ed

Col

lisio

n

Upgrading-A (P2 / P1): Crossings w ith Stop Signs / Crossings w ith No Stop Signs

Upgrading-B (P3 / P2): Crossings w ith Flashing Lights / Crossings w ith Stop Signs

Upgrading-C (P4 / P3): Crossings w ith Gates / Crossings w ith Flashing Lights

Figure 7.9: Effect of Number of Traffic Lanes on Predicted Collision Ratio when

Comparing Two Protection Types (Controlled by Annual Average Daily Traffic = 5000

vehicles; Daily Train Traffic = 20 trains; Maximum Timetabled Train Speed = 50 mph;

Highway Speed = 35 mph; and Number of Main Tracks = 1)

Highway Speed The ratios of predicted collisions among the four types of protection types as related

to highway speed are shown in Figure 7.10. Three observations are made from this

sensitivity analysis. Firstly, the ratios of expected collisions for all upgrading are

consistently lower than the value of 1.0 for all available range of highway speed.

This shows that if crossings are upgraded from ‘No-stop signs’ to ‘Stop signs’; or

from ‘Stop signs’ to ‘Flashing lights’; or from ‘Flashing lights’ to ‘Gates’, some

reduction in the number of collisions would occur irrespective of the highway speed.

The second observation is that highway speed has very little positive impact on the

benefit for all types of upgrading. Thirdly, it is noted that more collisions reduction

for Upgrading - A are expected regardless of highway speed than at other types of

crossings for the same controlled value of other parameters.

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Ratio of Predicted Collision Vs Highway Speed

0.000.200.400.600.801.00

15 30 45 60 75

Highway Speed

Rat

io o

f Pre

dict

ed

Col

lisio

n

Upgrading-A (P2 / P1): Crossings w ith Stop Signs / Crossings w ith No Stop Signs

Upgrading-B (P3 / P2): Crossings w ith Flashing Lights / Crossings w ith Stop Signs

Upgrading-C (P4 / P3): Crossings w ith Gates / Crossings w ith Flashing Lights

Figure 7.10: Effect of Highway Speed on Predicted Collision Ratio when Comparing

Two Protection Types (Controlled by Annual Average Daily Traffic = 5000 vehicles;

Daily Train Traffic = 20 trains; Maximum Timetabled Train Speed = 50 mph; Number of

Traffic Lanes = 2; and Number of Main Tracks = 1)

7.2.4 Effects of Upgrading Protec tion Types on Co llisions Related

to Railway Characteristics

Sensitivity of models predicting collision ratios related to the three railway

parameters (Daily train movement, Number of main tracks and Train Speed) by the

three upgrading types (Upgrading-A: From Protection type 1 to Protection type 2;

Upgrading-B: From Protection type 2 to Protection type 3; and Upgrading-C: From

Protection type 3 to Protection type 4) is examined below.

Daily Train Traffic Figure 7.11 depicts the ratios of predicted collisions among the four types of

protection types as related to Daily Train Traffic. Three observations emerge from

this sensitivity analysis. The first observation is that the ratios of expected collisions

for all upgrading are consistently lower than the value of 1.0 for all available range

of Daily Train Traffic. This indicates that if crossings are upgraded from ‘No-stop

signs’ to ‘Stop signs’; or from ‘Stop signs’ to ‘Flashing lights’; or from ‘Flashing

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lights’ to ‘Gates’, some reduction in the number of collisions would occur

irrespective of the volume of train traffic.

Ratio of Predicted Collision Vs Daily Train Traffic

0.000.200.400.600.801.00

10 50 100 150 200

Daily Train Traffic

Rat

io o

f Pre

dict

ed

Col

lisio

n

Upgrading-A (P2 / P1): Crossings w ith Stop Signs / Crossings w ith No Stop Signs

Upgrading-B (P3 / P2): Crossings w ith Flashing Lights / Crossings w ith Stop Signs

Upgrading-C (P4 / P3): Crossings w ith Gates / Crossings w ith Flashing Lights

Figure 7.11: Effect of Daily Train Traffic on Predicted Collision Ratio when Comparing

Two Protection Types (Controlled by Annual Average Daily Traffic = 5000 vehicles;

Maximum Timetabled Train Speed = 50 mph; Highway Speed = 35 mph; Number of Traffic

Lanes = 2; and Number of Main Tracks = 1)

Secondly, the model suggests that while it is always beneficial to upgrade crossings,

Daily Train Traffic has a slight positive impact on the benefit for the types of

Upgrading - B and Upgrading - C. Thirdly, the type of Upgrading - A has a negative

effect on reducing collisions by more than three times over the high range of Daily

Train Traffic (around 100). The fact that the majority of crossings with no-stop signs

have less volume of train traffic compared to crossings with stop signs may be one of

the possible reasons for this result.

Number of Main Tracks Figure 7.12 shows the ratios of predicted collisions among the four types of

protection types as related to number of main tracks. Three observations emerge

from this sensitivity analysis. The first observation is that the ratios of expected

collisions for all upgrading are consistently lower than the value of 1.0 for all

available ranges of number of main tracks. This suggests that if crossings are

upgraded from ‘No-stop signs’ to ‘Stop signs’; or from ‘Stop signs’ to ‘Flashing

lights’; or from ‘Flashing lights’ to ‘Gates’, some reduction in the number of

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collisions would occur irrespective of the number of main tracks. Secondly, the

number of main tracks has a slight positive impact on the benefit for all types other

than Upgrading - C. Thirdly, the type of Upgrading - C has a negative effect on

reducing collisions over the high range of main tracks (around 5). One possible

reason for this result is that the majority of crossings with flashing lights have fewer

numbers of main tracks compared to crossings with gates.

Ratio of Predicted Collision Vs Number of Main Tracks

0.000.200.400.600.801.00

1 2 3 4 5

Number of Main Tracks

Rat

io o

f Pre

dict

ed

Col

lisio

n

Upgrading-A (P2 / P1): Crossings w ith Stop Signs / Crossings w ith No Stop Signs

Upgrading-B (P3 / P2): Crossings w ith Flashing Lights / Crossings w ith Stop Signs

Upgrading-C (P4 / P3): Crossings w ith Gates / Crossings w ith Flashing Lights

Figure 7.12: Effect of Number of Main Tracks on Predicted Collision Ratio when

Comparing Two Protection Types (Controlled by Annual Average Daily Traffic = 5000

vehicles; Daily Train Traffic = 20 trains; Maximum Timetabled Train Speed = 50 mph;

Highway Speed = 35 mph; and Number of Traffic Lanes = 2)

Train Speed The ratios of predicted collisions among the four types of protection types as related

to train speed are shown in Figure 7.13. Three observations emerge from this

sensitivity analysis. Firstly, the ratios of expected collisions for all upgrading are

consistently lower than the value of 1.0 for all available range of train speed. This

suggests that if crossings are upgraded from ‘No-stop signs’ to ‘Stop signs’; or from

‘Stop signs’ to ‘Flashing lights’; or from ‘Flashing lights’ to ‘Gates’, some reduction

in the number of collisions would occur irrespective of the train speed. The second

observation is that train speed has very little positive impact on the benefit for all

types of Upgrading. Thirdly, it is noted that more collisions reduction for Upgrading

- B are expected regardless of train speed than at other types of crossings for the

same controlled value of other parameters. This shows that if crossings are upgraded

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from ‘Stop signs’ to ‘Flashing lights’, it would be expected there would be more

reduction in the number of collisions over all ranges of train speed.

Ratio of Predicted Collision Vs Maximum Train Timetabled Speed

0.000.200.400.600.801.00

20 40 60 80 100

Maximum Train Timetabled Speed

Rat

io o

f Pre

dict

ed

Col

lisio

n

Upgrading-A (P2 / P1): Crossings w ith Stop Signs / Crossings w ith No Stop Signs

Upgrading-B (P3 / P2): Crossings w ith Flashing Lights / Crossings w ith Stop Signs

Upgrading-C (P4 / P3): Crossings w ith Gates / Crossings w ith Flashing Lights

Figure 7.13: Effect of Maximum Timetabled Train Speed on Predicted Collision Ratio

when Comparing Two Protection Types (Controlled by Annual Average Daily Traffic =

5000 vehicles; Daily Train Traffic = 20 trains; Highway Speed = 35 mph; Number of Traffic

Lanes = 2; and Number of Main Tracks = 1)

7.3 Examining Models Predicting Consequences

When similar examination of sensitivity (as in the previous section) is carried out on

model predicting consequences by its constructed parameters individually, only one

of the parameters is considered as variable and the others are controlled by given

values. In this study, the controlled value for each parameter is selected as the

approximate mean value of relevant parameter for all crossing types. The groups of

risk factors and the controlled values of parameters in modelling are shown in

Table 7.2.

Table 7.2: Controlled Value for Parameters Constructing Consequence Prediction Models

Characteristic Parameter of Models Controlled Value

Highway Total Occupants in Vehicle 1

Railway Maximum Timetabled Train Speed 50 mph

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7.3.1 Effects of Highway Characte ristics on Four Protection Types

In the models predicting consequences, there was only one parameter related to

highway characteristics (Total occupants in vehicle) identified. Sensitivity of models

predicting consequences by this parameter is examined below.

Total Occupants in Vehicle Figure 7.14 depicts the relationship between the predicted consequences (equivalent

fatalities per year) versus Total occupants in vehicle for the four types of protection.

The predicted value of consequences at grade crossings increases as the number of

occupants increases. This implies that the total occupants in a vehicle may have a

negative effect on the safety of grade crossings regardless of type of protection.

However, the rate of consequences depends on the type of protection equipped at

crossings.

Predicted Consequences Vs Total Occupants in Vehicle

0.00

0.05

0.10

0.15

0.20

1 2 3 4 5 6

Total Occupants in Vehicle

Pre

dict

ed E

quiv

alen

tFa

talit

ies

Crossings w ith No Stop Signs (P1) Crossings w ith Stop Signs (P2)

Crossings w ith Flashing Lights (P3) Crossings w ith Gates (P4)

Figure 7.14: Effect of Total Occupants in Vehicle on Annual Consequences Prediction by

Protection Type (Controlled by Maximum Timetabled Train Speed = 50 mph)

7.3.2 Effects of Railway Character istics on Four Protection Types

In the models predicting consequences, there was only one parameter related to

railway characteristics (Maximum Timetable Train Speed) identified. Sensitivity of

models predicting consequences by this parameter is examined below.

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Train Speed Figure 7.15 illustrates the relationship between the predicted consequences

(equivalent fatalities per year) versus Train speed for the four types of protection. It

is noted that train speed has little positive effect on the consequences of collisions at

all crossings. It is also noted that more consequences of collisions are expected at

crossings with gates regardless of train speed than at other types of crossings for the

same controlled value of other parameters.

Predicted Consequences Vs Maximum Train Timetabled Speed

0.00

0.02

0.04

0.06

20 40 60 80 100

Maximum Train Timetabled Speed

Pre

dict

ed E

quiv

alen

tFa

talit

ies

Crossings w ith No Stop Signs (P1) Crossings w ith Stop Signs (P2)

Crossings w ith Flashing Lights (P3) Crossings w ith Gates (P4)

Figure 7.15: Effect of Maximum Timetable Train Speed on Annual Consequences

Prediction by Protection Type (Controlled by Total Occupants in Vehicle = 1)

7.4 Examining Models Predicting Safety Risk Index (SRI)

When similar examination of sensitivity (as performed in the previous sections) is

carried out on the model estimating safety risk index by its constructed parameters

individually, only one of the parameters is considered as variable and the others are

controlled by given values. In this study, the controlled value for each parameter is

selected as the approximate mean value of relevant parameter for all crossing types.

The groups of risk factors and the controlled values of parameters in modeling are

shown in Table 7.3.

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Table 7.3: Controlled Values for Parameters Constructing Safety Risk Index Models

Characteristic Parameter of Models Controlled Value

Highway

Annual Average Daily Traffic 5000 vehicles

Highway Speed 35 mph

Number of Traffic Lanes 2

Total Occupants in Vehicle 1

Railway

Daily Train Traffic 20 trains

Maximum Timetabled Train Speed 50 mph

Number of Main Tracks 1

7.4.1 Effects of Highway Characte ristics on Four Protection Types

In the models estimating safety risk index, there were four parameters related to

highway characteristics (Annual average daily traffic, Number of traffic lanes,

Highway speed and Total occupants in vehicle) identified. Sensitivity of models

estimating SRI by these four parameters is examined below.

Annual Average Daily Traffic (AADT) Figure 7.16 depicts the relationship between the estimated Safety risk index (SRI)

per year versus Annual average daily traffic for the four types of protection. The

estimated SRI at grade crossings increases as AADT increases. This implies that

highway traffic volume has a negative effect on the safety of grade crossings

regardless of type of protection. However, the rate of SRI depends on the type of

protection equipped at crossings.

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0.00

0.10

0.20

0.30

0.40

Est

imat

ed S

RI

Annual Average Daily Traffic

Annual Estimated Safety Risk Index Vs Annual Ave Daily Traffic

Crossings with No Stop Signs (P1) Crossings with Stop Signs (P2)

Crossings with Flashing Lights (P3) Crossings with Gates (P4)

Figure 7.16: Effect of Annual Average Daily Traffic on Estimation of SRI by Protection

Type (Controlled by Daily Train Traffic = 20 trains; Maximum Timetabled Train Speed =

50 mph; Highway Speed = 35 mph; Number of Traffic Lanes = 2; Total Occupants in

Vehicle = 1; and Number of Main Tracks = 1)

Grade crossings without any stop signs or any signals may have the highest rate of

increase followed by the crossings with stop signs; crossings with flashing lights; and

crossings with gates. This shows that highway traffic volume had an exceptionally

higher response on safety risk at no-stop sign grade crossings than those at crossings

with signs, flashing lights and gates.

Number of Traffic Lanes The relationship between the estimated Safety risk index per year versus Number of

traffic lanes for the four types of protection is depicted in Figure 7.17. It shows that

the number of traffic lanes has no impact on the safety risk at no-stop sign crossings

and has a slight positive response at crossings with flashing lights or gates. However,

the estimated safety risk at crossings with stop signs considerably increases with the

number of traffic lanes. It is noted that, regardless of the number of traffic lanes,

more safety risks are estimated at no-stop sign crossings (about four times higher)

compared with the other types of crossings for the same controlled value of other

parameters.

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0.00

0.05

0.10

0.15

0.20

0.25

Est

imat

ed S

RI

Number of Traffic Lanes

Annual Estimated Safety Risk Index Vs Number of Traffic Lanes

Crossings with No Stop Signs (P1) Crossings with Stop Signs (P2)

Crossings with Flashing Lights (P3) Crossings with Gates (P4)

Figure 7.17: Effect of Number of Traffic Lanes on Estimation of SRI by Protection Type

(Controlled by Annual Average Daily Traffic = 5000 vehicles; Daily Train Traffic = 20

trains; Maximum Timetabled Train Speed = 50 mph; Highway Speed = 35 mph; Total

Occupants in Vehicle = 1; and Number of Main Tracks = 1)

Highway Speed Figure 7.18 illustrates the relationship between the estimated Safety risk index per

year versus Highway speed (mph) for the four types of protection. It shows that

highway speed has no response on the safety risk at no-stop sign and gate crossings

and has a negligible effect at crossings with signs and flashing lights. It is noted that,

regardless of highway speed, more safety risks are estimated at stop sign crossings

(about eight times higher) compared with crossings with flashing lights or gates for

the same controlled value of other parameters. Safety risks at no-stop sign crossings

are about four times higher than crossings with stop signs.

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0.00

0.05

0.10

0.15

0.20

0.25

Est

imat

ed S

RI

Highway Speed

Annual Estimated Safety Risk Index Vs Highway Speed

Crossings with No Stop Signs (P1) Crossings with Stop Signs (P2)

Crossings with Flashing Lights (P3) Crossings with Gates (P4)

Figure 7.18: Effect of Highway Speed on Estimation of SRI by Protection Type

(Controlled by Annual Average Daily Traffic = 5000 vehicles; Daily Train Traffic = 20

trains; Maximum Timetabled Train Speed = 50 mph; Number of Traffic Lanes = 2; Total

Occupants in Vehicle = 1; and Number of Main Tracks = 1)

Total Occupants in Vehicle Figure 7.19 depicts the relationship between the estimated Safety risk index (SRI)

per year versus Total occupants in vehicle for the four types of protection. The

estimated SRI at grade crossings increases as the number of occupants increases.

This implies that a higher number of occupants have a negative effect on the safety

of grade crossings regardless of the type of protection. However, the rate of SRI

depends on the type of protection equipped at crossings. Grade crossings without any

stop signs or any signals have the highest rate of increase followed by the other

crossing types.

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0.00

0.10

0.20

0.30

0.40

0.50

Est

imat

ed S

RI

Total Occupants in Vehicle

Annual Estimated Safety Risk Index Vs Total Occupants in Vehicle

Crossings with No Stop Signs (P1) Crossings with Stop Signs (P2)

Crossings with Flashing Lights (P3) Crossings with Gates (P4)

Figure 7.19: Effect of Total Occupants in Vehicle on Estimation of SRI by Protection

Type (Controlled by Annual Average Daily Traffic = 5000 vehicles; Daily Train Traffic = 20

trains; Highway Speed = 35 mph; Number of Traffic Lanes = 2; Maximum Timetabled Train

Speed = 50 mph; and Number of Main Tracks = 1)

7.4.2 Effects of Railway Characte ristics on Four Protection Types

There were three parameters related to railway characteristics (Daily train movement,

Number of main tracks and Train Speed) identified in the models estimating safety

risk index. Sensitivity of models estimating SRI by these parameters is examined

below.

Daily Train Traffic Figure 7.20 depicts the relationship between the estimated Safety risk index per year

versus Daily train traffic for the four types of protection. The estimated safety risk

index at grade crossings increases, as train traffic increases for all grade crossings

except with no-stop signs. This implies that train traffic volume has a negative effect

on the safety of grade crossings other than no-stop sign types. However, the rate of

SRI increase depends on the type of protection equipped at crossings. Grade

crossings with stop signs or signals have the highest rate of increase followed by

crossings with flashing lights and then crossings with gates. This means that train

traffic volume has an exceptionally higher effect on safety risk at stop signs or

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signals grade crossings than those at crossings with flashing lights and gates. It is

noted that train traffic volume has no effect on the safety risk at no-stop sign

crossings. The fact that the majority of no-stop sign crossings have less volume of

train traffic may be one of the possible explanations for this result.

0.000.050.100.150.200.250.30

Est

imat

ed S

RI

Daily Train Traffic

Annual Estimated Safety Risk Index Vs Daily Train Traffic

Crossings with No Stop Signs (P1) Crossings with Stop Signs (P2)

Crossings with Flashing Lights (P3) Crossings with Gates (P4)

Figure 7.20: Effect of Daily Train Traffic on Estimation of SRI by Protection Type

(Controlled by Annual Average Daily Traffic = 5000 vehicles; Maximum Timetabled Train

Speed = 50 mph; Highway Speed = 35 mph; Number of Traffic Lanes = 2; Total Occupants

in Vehicle = 1; and Number of Main Tracks = 1)

Number of Main Tracks The relationship between the estimated Safety risk index per year versus Number of

main tracks for the four types of protection is depicted in Figure 7.21. It shows that

the number of main tracks has no effect on the safety risk at any crossings other than

gate types, which has little effect. It is noted that more safety risks at no-stop sign

crossings are estimated regardless of main tracks than at other types of crossings for

the same controlled value of other parameters.

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0.00

0.05

0.10

0.15

0.20

0.25

Est

imat

ed S

RI

Number of Main Tracks

Annual Estimated Safety Risk Index Vs Number of Main Tracks

Crossings with No Stop Signs (P1) Crossings with Stop Signs (P2)

Crossings with Flashing Lights (P3) Crossings with Gates (P4)

Figure 7.21: Effect of Number of Main Tracks on Estimation of SRI by Protection Type

(Controlled by Annual Average Daily Traffic = 5000 vehicles; Daily Train Traffic = 20

trains; Maximum Timetabled Train Speed = 50 mph; Highway Speed = 35 mph; Total

Occupants in Vehicle = 1; and Number of Traffic Lanes = 2)

Train Speed Figure 7.7 illustrates the relationship between the estimated Safety risk index per

year versus Train speed (mph) for the four types of protection. It is noted that train

speed has no effect on the safety risk at crossings with gates, and medium effect on

crossings with no-stop signs. Other types of crossings have little effect on safety. It is

noted that more safety risks at no-stop sign crossings are estimated regardless of train

speed than at other types of crossings for the same controlled value of other

parameters.

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0.000.020.040.060.080.100.120.14

Est

imat

ed S

RI

Maximum Train Timetabled Speed

Annual Estimated Safety Risk Index Vs Max Train Timetable Speed

Crossings with No Stop Signs (P1) Crossings with Stop Signs (P2)

Crossings with Flashing Lights (P3) Crossings with Gates (P4)

Figure 7.22: Effect of Maximum Timetabled Train Speed on Estimation of SRI by

Protection Type (Controlled by Annual Average Daily Traffic = 5000 vehicles; Daily Train

Traffic = 20 trains; Highway Speed = 35 mph; Number of Traffic Lanes = 2; Total

Occupants in Vehicle = 1; and Number of Main Tracks = 1)

7.5 Summary

As part of overall impact (sensitivity) analysis of key factors on risk at railway

crossings, preliminary analysis of various factors is carried out and outlined, by

identifying which parameters are sensitive and important to the prediction of

imprecision - how sensitive a predictive model is to change in the values of the

parameters and to change in the structure of the model. It is shown that the impact

analysis enables the decision makers and operations managers to identify the impact

of significant factors that influence risks at grade crossings.

The sensitivity analysis of accident prediction models carried out in this research is

consistent with those reported in the published literature. Furthermore, sensitivity

analyses of other two types of models (Consequence prediction and Severity risk

index estimation) are carried out and the results of impact analysis were discussed

and presented. In summary, all three types of models (Accidents prediction,

Consequence prediction and Severity risk index estimation) were examined using

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impact analyses for better understanding of key variables on risk at railway

crossings. Negative Binomial model was selected, based on the results of impact

analysis for its suitability and simplicity, and because the EB model was considered

to be too complex to perform the impact analysis on frequency of accidents, as it

requires the accidents history of each location.

Examination related to sensitivity analysis on the accidents prediction models

showed that the highest risk related parameter, which explains accidents at public

grade crossings with all types of protection, is highway traffic volume (AADT).

Daily train traffic volume and the number of traffic lanes show the second and third

highest risk related parameters respectively for all crossings except those with ‘No

Stop Signs’ protection. Train speed showed medium positive impact on safety on all

crossings except those with ‘Gates’ protection. The number of main tracks indicated

moderate impact on safety at crossings with ‘Gates’ protection. Safety at crossings

with the protection of ‘Stop Signs’ and ‘Flashing Lights’ are also slightly affected by

highway speed. Testing on the consequences prediction models showed that the

highest risk related parameter, which explains consequences at public grade

crossings with all types of protection, is the number of occupants in a vehicle. Train

speed indicated moderate impact on safety at all crossings. However, examining the

sensitivity of all parameters (highway traffic volume, daily train traffic volume,

number of main tracks, train speed, number of traffic lanes and highway speed) in

the severity risk index estimation models showed the same results, which were

obtained from the accidents prediction models. The number of occupants in a vehicle

showed negative effect on the safety of grade crossings regardless of type of

protection.

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Chapter 8

Conclusions and Recommendations

8.0 Introduction

Overall, the main focus of this study is to develop an improved risk assessment model

for railway grade crossings through various stages as outlined in Section 1.7 of

Chapter 1 – Overview of Organisation of the Study. Based on conclusions drawn

from a literature review highlighting the need for an improved methodology for

assessing safety risks at railway grade crossings using a single safety risk index,

Chapter 2 presented an overview of rail safety management, leading to identification

of research problems. Various rail safety issues, problems and all micro-level factors

that could contribute to rail accidents are discussed in this Chapter. An appropriate

methodology for combining different key performance indicators, with a view to

assessing rail safety risks was then developed and presented in Chapter 3.

Conclusions drawn from the literature review including identification of research

problems and overview of rail safety management formed the basis for initial model

selection using existing models ranging from deterministic models to statistical

models. Chapter 4 explained the procedures for extraction and utilisation of rail

accidents data and inventory information to evaluate rail safety risks by developing

risk assessment models. Chapter 5 described the development of appropriate models

for predicting accidents frequencies and consequences, and explained the theoretical

framework of the models with the support of the key performance indicators. Chapter

6 generated a single composite risk index (Safety Risk Index) to assess and prioritise

rail safety performances at grade crossings using the predictions obtained in

Chapter 5. Models were tested and outcomes of those testing were reported in

Chapter 5. Comprehensive statistical testing of those models confirmed validity of

developed models for future use in similar situations. This was followed by

development of a safety risk index based on individual models of predicting accidents

and consequences, as reported in Chapter 6. Sensitivity analysis, including some

qualitative assessment, was performed as part of model validation and reported in

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Chapter 7. The observations from this study provide a means to identify the

influences of relevant factors on prediction of accident frequencies, consequences

and safety risk.

Given the various stages of this research involving comprehensive literature review

reported in Chapter 2, an overview of rail safety management, research problem

definition and formulation, data source selection, data selection with data cleansing

and eventual model development, this chapter presents conclusions reported earlier,

as an integral part of overall conclusions of the research study. This chapter also

discusses objectives achieved and contributions (both theoretical and practical)

made as a result of the outcome of this research. It clearly indicates the benefits and

limitations of the research study. Finally, this chapter outlines potential future

research work, which can make a further contribution to the field of research

undertaken in this research study.

8.1 Overview of Research Findings

This chapter provides a brief summary of research contributions and conclusions

made along with research findings reported earlier. The aim of this research is to

provide a strong basis for the initial process of safety improvement at railway-

highway grade crossings. The research work carried out and reported in this thesis is

considered to be an integral part of a comprehensive international multi-stage safety

management program, which generally consists of five interconnected initiatives:

• Separate models for prediction of accidents and consequences at grade

crossings were developed;

• Grade crossings, where the potential risk of accidents is unacceptably high,

were identified;

• Grade crossings, where the potential risk of consequences is unacceptably

high, were identified;

• A single composite index (Safety Risk Index), using the prediction of

accidents and consequences to assess and prioritise the risk potential at the

crossings, was developed;

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• With the estimated values of the Safety Risk Index, all ‘Black-spot’crossings,

where the overall potential risk is unacceptably high, were identified.

These five initiatives carried out as part of this research are discussed in detail and

the conclusions associated with each initiative is summarised in this chapter. These

initiatives assist in the development of comprehensive safety intervention programs

at state and national levels that includes prioritisation of countermeasures at high-risk

crossings by reviewing the causes of accidents and available control measures at

these locations.

Given the increasing number of rail infrastructures and resulting railway grade

crossings across the globe, accidents at railway-highway grade crossings are

considered to be a critical rail safety issue associated with the rail safety management

area. Although these accidents generally arise from several factors that are largely

outside of railroad control, the rail industry is committed to making enormous efforts

aimed at sharply reducing the frequency and consequences of grade crossing

accidents. As stated in the Chapter 2, to address the safety issues at grade crossings

under the light of rail safety management, this study assists the railway and highway

industries by means of:

“Exploring a new improved method, to develop evaluation techniques and

procedures to assess and prioritise safety risks at grade crossings, which can be used

in support of the effective rail safety management”.

Having identified the need for improvement in assessing safety risks at grade

crossings, a number of various models for predicting accidents frequencies and

accidental consequences were initially developed using many microscopic indicators

for each type of protection at crossings. Using a Generalized Linear Models (GLMs)

technique available on statistical software and particularly SPSS, appropriate models

were generated and validated with statistical tools such as Pearson correlation, t-

ratio, Multiple correlation and Scaled deviance for goodness-of-fit on models. By

adopting a two-dimensional graphical representation with the estimation of accidents

frequencies and accidental consequences, a Safety Risk Index (SRI) model was then

developed to assess and prioritise risks at grade crossings. The developing

procedures of the safety risk assessment models and their results are briefly

summarised as follows.

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8.1.1 Accident Frequency Prediction Model

In the development of an accident prediction model, it was initially found that

Negative Binomial (NB) distribution produced better results when compared with

that of the Poisson distribution method. However the Empirical Bayesian method,

which adjusted to the NB model, finally yielded even better predictions as it partially

reflects historical observations. From this study, it can be concluded that the

expected accident frequency is best modelled using the EB method with separate

expressions for four different types of protection. In this case, the number of

accidents occurring at each crossing is used as a dependent variable in the model of

accident prediction. Independent variables of daily train movement, annual average

daily traffic, maximum timetable train speed, highway speed, number of main tracks

and number of traffic lanes were initially considered in the process of developing the

models. The final models of accident frequency expressions for each type of

protection are summarised in Table 8.1.

Table 8.1: EB Modelling Equations for Accident Frequency Prediction with Explained

Variables by All Protection Types

Protection Type EB modelling equation for expected accidents frequency at a grade crossing for 5 years period Description of V ariables

Type 1 (No Signs or No

signals)

(AADT)]Ln *0.695 MTTS * 0.030 -6.369[*4421.0*5579.0),(ˆ

1

+++= eyyYEG

DT- Daily Train Movement

AADT- Annual Average Daily Traffic

MTTS - Max Timetable Train Speed

HS- Highway Speed

MT- Number of Main Tracks

TL- Number of Traffic Lanes

y- Number of accidents (5 years) in

history

Type 2 (Stop Signs or

Cross-bucks) (AADT)]Ln *0.300 (DT)Ln * 0.484 TL * 0.313HS * 0.014 MTTS * 0.015 -5.822[

*4547.0*5453.0),(ˆ2

++++++= eyyYEG

Type 3 (Signals, Bells

or Warning Devices) (AADT)]Ln *0.261 (DT)Ln * 0.359 TL * 0.252HS * 0.010 MTTS * 0.013 -5.750[

*4181.0*5819.0),(ˆ3

++++++= eyyYEG

Type 4 (Gates or Full

Barrier) (AADT)]Ln *0.173 (DT)Ln * 0.248 TL * 0.167 MT * 0.185 -4.383[

*4136.0*5864.0),(ˆ4

+++++= eyyYEG

The statistical analysis concluded that the traffic exposure (i.e. Annual average daily

traffic and Daily train movement) is the most important factor in constructing

accident frequency models (Refer Table 8.2). Within the traffic exposure factor,

Annual average daily traffic is the most contributing parameter for all protection

types of railway-highway grade crossings. The parameters of Train speed and

Number of traffic lanes are found to provide a significant explanation for differences

in the expected number of accidents. Number of traffic lanes affects the prediction of

accidents at all crossings except the protection type of “No signs or no signals”.

Train speed is a significant contributing parameter on the prediction of accidents at

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all crossings except the protection type of “Gates or Full Barrier”. Highway speed

also plays an important role in accident prediction at crossings with “Stop signs or

cross-bucks” and “Signals, bells or warning devices”. Finally, Number of main

tracks has little impact on accidents at crossings with “Gates or Full Barrier”. By

referring R-square (R2) values, on average, these models are explained

approximately 50% of the systematic variation in accidents at all public grade

crossings.

Table 8.2: Impact Effect of Railway and Highway Characteristics on Accident Prediction

by Protection Type

FACTOR

VARIABLE

EFFECT OF IMPACT ON ACCIDENTS PREDICTION BY PROTECTION TYPE

1. No Signs or No

Signals

2. Stop Signs or

Cross-bucks

3. Signals, Bells or

Warning Devices

4. Gates or Full

Barrier

Railway Daily Train Movement N/A High Medium Low

Number of Main Tracks N/A N/A N/A Low

Train Speed Medium Low Low N/A

Highway Annual Average Daily Traffic High Medium Low Low

Number of Traffic Lanes N/A Medium Low Low

Highway Speed N/A Low Low N/A

8.1.2 Accident Consequences Prediction Model

Fatalities, personal injuries, and property and vehicle damage were mainly

considered as accident severity consequences. Since these consequences contribute

disproportionately to accident severity, each of them had to be weighted according to

their reported average costs in the past. Average costs for the severity consequences

in the 1995 were reported by the United States National Safety Council cost

estimates from California Life-cycle Benefit / Cost Analysis Model (California

Department of Transportation 1999). These costs form a uniform value or

“yardstick” by which different accident consequences can be compared. Based on

these average costs, a single consequence score (known as “Equivalent Fatality

Score”) was initially developed. As this score is associated with different levels of

accident severity (including fatality, injury and property and vehicle damage), the

full spectrum of consequences associated with each accident was represented and

incorporated into final process for identification of Black-spots. The equation for

estimating the Equivalent Fatality Score is:

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EFS = 1.0*FAT+0.0243*INJ+ (0.0229*PVD/61950)

where:

EFS - Equivalent Fatality Score;

FAT - Number of fatalities;

INJ - Number of Injuries; and

PVD - Property and vehicle damage in dollars.

The same processes and techniques explained earlier for developing accident

frequency models were repeated for generating the models for prediction of

accidental consequences. Separate models for each type of protection of four classes

of protection were obtained. In this case, the equivalent fatality score associated with

each crossing was utilised as a dependent variable instead of using a number of

accidents in the accidents prediction models. Independent variables of maximum

timetable train speed, highway speed, number of main tracks, number of traffic lanes,

track crossing angle and total occupants in a vehicle were initially considered in the

process of developing the models. As in the case for accidents frequency prediction,

different prediction models were investigated for accident consequences using the

GLM method.

Table 8.3: EB Modelling Equations for Accident Consequences Prediction with Explained

Variables by All Protection Types

Protection Type EB modelling equation for expected equivalent fatalities per an

accident at a grade crossing

Description of Variables

Type 1 (No Signs or

No signals) ]MTTS * 0.046 TOV * 0.789 -5.692[

*2846.0)|(*7154.0)]|(),|[(ˆ11

+++= eGG

yCyCYCE MTTS - Max Timetable Train

Speed

TOV - Total Occupants in

Vehicle

y- Number of accidents (5

years) in history

C- Consequences (Equivalent

Fatalities) in history

Type 2 (Stop Signs or

Cross-bucks) ]MTTS * 0.039 TOV * 0.474 -4.800[

*3797.0)|(*6203.0)]|(),|[(ˆ22

+++= eGG

yCyCYCE

Type 3 (Signals, Bells

or Warning Devices) ]MTTS * 0.035 TOV * 0.415 -4.410[

*3402.0)|(*6598.0)]|(),|[(ˆ33

+++= eGG

yCyCYCE

Type 4 (Gates or Full

Barrier) ]MTTS * 0.022 TOV * 0.403 -3.548[

*4402.0)|(*5598.0)]|(),|[(ˆ44

+++= eGG

yCyCYCE

It was initially found that Negative Binomial distribution yielded better results when

compared to the Poisson distribution method. However the Empirical Bayesian

method, which adjusted to the EB model, finally yielded even better predictions. It

was concluded that the expected accidental consequences is best modelled using the

EB method with separate expressions for four different types of protection. The final

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models of accident consequences expressions for each type of protection are

summarised in Table 8.3. The consequence prediction model assumes a prior

occurrence of an accident. The NB accident consequences models reveal that

severity (expected equivalent fatalities) of an accident depends on two parameters

(Total occupants in vehicle and Maximum timetable train speed) for crossings with

all four protection types. Total occupants in vehicle play a major role in estimating

accidental consequences (Refer Table 8.4). Maximum timetable train speed

contributes a minor effect on the prediction of accidental severities. By referring R-

square (R2) values, on average, these models explain nearly 45% of the systematic

variation in accidental consequences at all public grade crossings.

Table 8.4: Impact Effect of All Factors on Consequences Prediction by Protection Type

FACTOR VARIABLE

EFFECT OF IMPACT ON CONSEQUENCES PREDICTION BY PROTECTION TYPE

1. No Signs or No

Signals

2. Stop Signs or

Cross-bucks

3. Signals, Bells or

Warning Devices

4. Gates or Full

Barrier

Railway Train Speed Medium Medium Medium Medium

Highway Total Occupants in Vehicle High High High High

8.1.3 Estimation of Safety Risk Index (SRI)

In order to assess the risk at each crossing, a single risk matrix method was initially

developed. By combining the predictions on accidents frequencies and the

consequences, an approach was developed to calculate the risk at grade crossings

within each protection type. By this approach, the product of estimated accidents and

estimated consequences will enable risk assessment at each crossing by means of a

“Safety Risk Index” score. In this method, the Safety Risk Index estimates the

number of equivalent fatalities sustained for the five-year period. For a given

crossing:

Fatalities EquivalentAccidents ofNumber

Fatalities Equivalent*Accidents ofNumber

y)]|[E(c esConsequencEstimated*y)][E(m,AccidentsEstimated )(Index Risk Safety

==

=ℜ

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8.1.4 Black-Spots Identified Using Safety Risk Index It is considered that higher risky crossings (Black-spots) fall on or above the

threshold curve (X*Y = oℜ ) in the safety risk index graph (Figure 8.1). The crossings

falling below the threshold curve are assumed to be relatively less risky. Black-spot

identification is therefore purely dependent on the threshold value of SRI.

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Pre

dict

ed C

onse

quen

ces

(Equ

ival

ent F

atal

ities

per

A

ccid

ent [

Y])

Number of Predicted Annual Accidents (X)

447 Black-Spots Identified within all Protection Types

447 Black-spots identified above Safety Risk Index Threshold Curve with SRI value of 0.15

 

Figure 8.1: 447 Basic Black-Spots identified in All Protection Types of Grade Crossings

However, it is a task for us to choose the optimal value for threshold. Basically, this

critical value relates to the number of crossings suggested to enhance safety at

minimal cost of intervention. As the number of crossings depends on budgetary

constraints, a great deal of study on cost benefit analysis while considering several

countermeasures for intervention will be required to determine the critical value of

threshold for each protection type of crossing. As this type of analysis is not feasible

at this stage, the following method is adopted to compute the threshold values. The

Safety Risk Index of each crossing within a protection type was initially calculated.

The standardised scores for all Safety Risk Indexes were then computed. Finally, the

number of high risk crossings was identified at different scores such as 1,2,3... and so

on. This procedure was repeated for all types of protection. It is noted that the

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number of Black-spots identified entirely depends on the standardised scores

associated with the Safety Risk Index. In this study, the SRI value of 0.15 that relates

to the standardised score of 4 has been selected as a basic threshold, and there were

447 grade crossings identified accordingly as basic Black-spots. The safety risk

details of these Black-spots are listed earlier in Table 6.6.

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Pre

dict

ed C

onse

quen

ces

(Equ

ival

ent F

atal

ities

pe

r Acc

iden

t [Y

])

Number of Predicted Annual Accidents (X)

Worst Black-Spots Identification within all Protection Types

Safety Risk Index Threshold Curve 1 (X*Y=0.15) Safety Risk Index Threshold Curve 2 (X*Y=0.30)

89 Worst Black-spots identified above Safety Risk index Threshold Curve 2

447 Black-spots identified above Safety Risk index Threshold Curve 1

 

Figure 8.2: Worst Black-Spots identification in All Protection Types of Grade Crossings

Within the 447 basic Black-Spots, worst Black-Spots can also be identified (depends

on budgetary constraints) by increasing the threshold values of SRI. For the purpose

of demonstration, another group of Black-Spots was identified (Figure 8.2). In this

group, the 89 worst Black-Spots were recognised with respect to a higher threshold

value of 0.30 that relates to the standardised score of 8. This process of selecting the

number of worst Black-Spots will be extended further. For example, the number of

worst Black-Spots 447, 89, 22, 6, 4 and 1 were selected by the SRI threshold value of

0.15, 0.30, 0.45, 0.60, 0.75 and 0.90 respectively. It is shown in the Figure 8.3.

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1 2 3 4 5 6

SRI Threshold Value 0.15 0.30 0.45 0.60 0.75 0.90

Number of Blackspots 447 89 22 6 4 1

447

89

226 4 1

0

50

100

150

200

250

300

350

400

450

500

Num

ber o

f Bla

ck-S

pots

Iden

tifie

d

SRI Threshold Value

Number of Black-Spots Identified as per SRI Threshold Value Selected

Figure 8.3: Number of Worst Black-Spots Identified as per SRI Threshold Value Selected

8.2 Contributions of Research Study

There are several safety risk preventive measures to reduce potential accidents risks

at grade crossings such as community education and awareness, train crew education,

grade crossing safety technology, vegetation control, signal and track inspection and

maintenance, grade crossing closure, installation of warning devices, surveillance,

enforcement, fencing for enclosing rights of way and grade separation. Through the

application of these safety risk preventive measures, the global railway industry has

become reasonably safe in recent years. However, at this time the number of

passengers is rising at an unprecedented rate, freight traffic has grown and is set to

expand even further, and performance is improving. This bears out what the Rail

sector has always known that high standards of performance and safety are

inextricably linked. It provides what passengers and customers expect, while creating

the essential condition for growth in traffic. As the authority for maintaining safety,

the Rail sector needs to assure itself and the community (the public, passengers and

employees) that safety risks are being managed at levels that are “As Low As

Reasonably Practicable”. In general terms, a Rail SMS means a holistic, systematic

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and optimal way of managing and controlling risks in the rail industry in order to

achieve desired safe outcomes in a sustainable way.

This research study aimed to gather, integrate and summarise available information,

data and knowledge on rail safety into measurable indicators, which can be then

converted into a single meaningful value. In this study “Grade crossings safety

evaluation”, which is one of the major initiatives of safety measures in the rail

industry, was taken into consideration and analysed. In order to improve the safety

level of railway-highway grade crossings, the study established an improved

appropriate methodology to develop and to construct a ‘Safety Risk Index (SRI)’.

This generic index is generated with reasonably large amounts of information from

available sources into measurable indicators, which may be then an easier format to

assess and to rank the safety risk status at grade crossings nationally. The index is

simple and easy to understand. The developed models provide a means to calculate

risk assessments and to rank rail safety at different locations. Therefore the models

are capable of increasing awareness of rail safety issues and problems among the rail

safety policy makers and rail users. Among other rail safety issues, railway-highway

accidents continue to be a major problem worldwide, both from the public health and

socio-economic perspectives. These collisions are a source of concern for regulators,

railway authorities and the public.

This study suggests a new improved risk-based methodology to assess and then to

prioritise the risks at grade crossings. The research was performed for rail safety

appraisal through the development and application of suitable accidents and

consequences prediction models for railway grade crossings, and by combining these

models to identify Black-Spots (worst dangerous locations). Data used in the study to

build the models is based on accidents and inventory statistical information published

by United States Department of Transportation Federal Railroad Authority (USDOT

FRA). The study was supported by data from 209,975 grade crossings selected from

all states in the USA. A wide range of traffic and geometric characteristic

information together with the corresponding accident data for each crossing for the

five-year period 2001-2005 was utilised in the model development process. Potential

explanatory variables were tested and largely identified from initial analysis of the

accident characteristics and associated factors. Generalized Linear Poisson and

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Negative Binomial Models for predicting accidents and consequences were initially

developed using the SPSS Version 15 package. The final models (Empirical

Bayesian) were then generated and evaluated separately for different protection types

of crossings. The study offers a quantitative risk assessment method to achieve safety

improvement at grade crossings, through seven major interconnected steps as:

• Developing appropriate models for predicting accident frequencies;

• Developing appropriate models for predicting consequences per accidents;

• Identifying crossings where the potential risk of accidents is unacceptably

high;

• Identifying crossings where the potential risk of consequences is

unacceptably high;

• Developing a single composite index (Safety Risk Index) using the prediction

of accidents and consequences to assess the risk potential at crossings;

• With the estimated values of Safety Risk Index (SRI), identifying ‘Black-

spot’crossings where the overall potential risk is unacceptably high; and

• Analysing the major factors causing accidents and consequences.

By successfully performing the above-mentioned risk assessment activities, this

study assists the Rail sector to conduct further steps such as developing

comprehensive safety intervention programs at state and national levels that includes

prioritisation of countermeasures at high-risk crossings. With the final Safety Risk

Index (SRI) model developed, safety risks at the different level crossing locations

can easily be calculated, compared and prioritised directly.

8.3 Benefits of Research Study

The proposed risk assessment model can be useful for researchers work in the

broader areas of improvement analysis of rail-road level crossing safety. It can also

be of interest to railway and highway organisations, as the index shows the scale of

current issues and problems that they were perhaps not aware of. In addition,

government policy makers can use this index to identify and prioritise the most risky

level crossing locations in their country, and to make appropriate policies, strategies

and intervention programs in order to minimise the risks to as low a level as possible

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at the most dangerous locations. The above-mentioned reasons suggest that the

Safety Risk Index (SRI) may be considered a significant tool in determining and

prioritising safety risks at grade crossings in any country.

Overall, the outcomes from this research are very encouraging in risk assessment

techniques under the light of rail safety management. The quantitative type SRI

index developed in this study is very promising and has the potential to be a major

tool for safety risk assessment at grade crossings. However, there may be more

possibilities in the future to extend this analytical research and its applications using

quality data and including more appropriate indicators in the models development.

8.4 Research Limitations

This research has some limitations which must be taken into consideration when

evaluating research findings and their implications for management. Firstly, the risk

assessment models developed in this study are based on a US data set (railway

inventory, accidents and consequences). This is mainly due to unavailability of

complete data set in Australian context, with required information on all indicators

for assessing risk at grade crossings. Even though the proposed approach and models

developed are considered to be generic for risk assessment at grade crossings in any

country, the models generated are considered to be more appropriate in the US

environment. In order to make models suitable to the Australian environment, rail

and other relevant organisations need to capture data and information on all

appropriate indicators. Furthermore, the Safety Risk models developed using US data

have to be re-developed and re-examined prior to use in the Australian environment

when required data and information are collected and available for public use.

Secondly, the status of some records on appropriate indicators in the US data shows

either incomplete or insufficient or missing information. In this case, the problematic

indicators were not considered in the analysis. There may be room for improvement

on models, if we had several indicators with high quality information.

Thirdly, this study is limited to risk assessment analysis based on the occurrence of

“accidents” at individual public grade crossings. Accidents within station or yard

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premises and non-crossing locations, those due to trespassing or suicides are not

included in this study. The analysis does not also consider the occurrence of "near

misses" since they are not normally reported in the occurrence database. Near miss

incidents represent breaches in safety that does not result in accidents. Adoption of

near miss incidents will certainly enhance the quality of models.

Finally, it was assumed in this study that both accident frequency and consequence

risks are mutually exclusive or independent of one another when the final risk

assessment model.

8.5 Recommendations

Although the author would like to test and validate models using local data (accident

and consequences in an Australian context), it is not the case here, given very limited

data in local context. Furthermore, the inventory data and information (which

contains the crossing characteristics such as highway traffic exposure, train

movement, train speed, highway speed, number of tracks, number of traffic lanes and

track crossing angle, etc.) at crossings is neither available nor accessible to the

public. Author strongly recommends that this type of information should be captured

and recorded by the relevant organisations, and made accessible to the public. In

future, Author hopes that relevant Australian organisations will develop a set of

major indicators in the accidents database and regularly update the information to

satisfy future data needs. However, in this study, Author eventually decided to use

the combined railway-highway grade crossing inventory and accident databases

provided by United States Department of Transportation Federal Railroad Authority

(USDOT FRA). This data is available to the public on the Internet and can be

downloaded on request. The period of five years (2001-2005) was chosen for the

analysis, and it was noted that in this period the inventory database contains an

inventory of 394,396 railway-highway crossings for all states in the USA including

information on highway and railway geometric characteristics, traffic volumes and

selected train operating features. The accident database includes information on

collision occurrence at some of these crossings for the past few years. The inventory

and occurrence databases share a common reference number that permits linkage of

each collision occurrence to public crossings specified by Crossing ID number.

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There are basic reasons why a separate safety risk model needs to be developed for

Australian data as distinct from the US model, which was developed in this study.

The safety risk model resulting estimates at each crossing were subsequently

aggregated according to four types of protection at the grade crossings in the US and

various types of crossing characteristics such as highway traffic exposure, train

movement, train speed, highway speed, number of tracks and number of traffic lanes.

As the characteristics, environment, situation and nature in Australia vary

considerably from the US, the predicted results may differ significantly from the

observed values, suggesting that the US model does not adequately reflect the

Australian data. Therefore, the transferability of safety risk models developed in this

study is to be re-examined when applied to grade crossing accidents reported in the

Australian data. This may be especially true in the case of casualty crossing

accidents. As a result, new risk prediction models based on Australian accident and

consequences data may have to be developed.

As grade crossings are the interfaces of Rail sector and Road sector, the safety risks

at these locations should jointly be assessed by both organisations. It would be useful

if organisations such as RailCorp - NSW and Road Traffic Authority (RTA) are

involved in the development of SRI models. Additionally, they can enhance their

performances in generating collaborative research activities with Australian

universities to create new methodologies and approaches to assess the risks in future.

8.6 Future Research

The Safety Risk Index (SRI) model developed in this study requires continuous

quality improvement, in order to allow for changes to rail infrastructure landscape. It

is recommended that the proposed models are thoroughly examined and strengthened

by accommodating those changes so prediction of accidents, consequences and

safety risk can be more accurate. Therefore, some of the suggestions that can

improve overall applicability of proposed models in the future, include the following.

The SRI models needs to be examined with data obtained from different kinds of

countries (developing and developed) worldwide. This process will determined

whether the results obtained from SRI models may be globally generalised. For

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example, as indicated earlier, this study is based on US accidents statistical data. It

may not be appropriate to use the same SRI models in Australia unless the models

are tested with Australian accidents statistical data.

It was found that the status of some records on appropriate indicators in the US data

shows either incomplete or missing information. In this case, the problematic

indicators were not considered in the analysis. For example, as more than a half of

the records within the indicator of “number of persons involved in accident” were

missing, this indicator was totally omitted from the analysis. More sophisticated or

robust statistical analysis and modelling may be used to consider these

missing/incomplete records and/or the inflated nature of some variables.

The new version of SRI may need more comprehensive data for a larger number of

indicators with high quality of information. There may be several unknown factors

playing a major role in developing an SRI. Unfortunately the majority of these

factors are not currently available in the data used so far. For example, this study is

limited to risk assessment analysis based on the occurrence of “accidents” at

individual public grade crossings. The analysis does not consider the occurrence of

"near misses" since they are not normally reported in the occurrence database. Near

miss incidents represent breaches in safety that does not result in actual accidents. It

may be more accurate in results, if a "near misses" indicator is included in the

analysis.

The risk models would show more accurate results if future research dealt with

subjective indicators. For example, the information on the status of whether ‘train

hits vehicle’ or ‘vehicle hits train’ is not available in the database. In the case of 'train

hits vehicle', the impact on the vehicle is high and therefore the severity of

consequences on persons occupying the vehicle will be high. Additionally, there may

be a possibility of derailment, which causes a high severity of consequences on

persons occupying the train. Conversely, if a vehicle hits a train the severity may be

low in comparison. If this indicator was available in the database, it would have been

taken into consideration in the development of risk model.

It is beneficial to improve accuracy on the results of SRI. This can be done by

continuously investigating new appropriate methodologies and their applications in

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the development of models. This process consists of selecting more appropriate

indicators, omitting less appropriate indicators, choosing suitable weight assessment

between indicators, etc. For example, in the development of model predicting

accidental consequences, the weight assessment for “Equivalent Fatality Score”

(between fatalities, personal injuries, and property and vehicle damage) was

established on the basis of a report (the United States National Safety Council cost

estimates from California Life-cycle Benefit / Cost Analysis Model) published in

1995. We can improve the accuracy of the results of the SRI if the latest figures on

weight assessment (if the information is available) are included in the analysis.

It is a most difficult task to establish an objective threshold value for a safety risk

assessment. This critical value relates to the number of crossings suggested to

enhance safety at minimal cost of intervention. As the number of crossings depends

on budgetary constraints, a great deal of study on cost benefit analysis, while

considering several countermeasures for intervention, will be required to determine

the critical value of threshold for each protection type of crossing. However, as this

type of analysis is not feasibly available at this stage, for the demonstration purposes

an alternative method (dealing with standardised scores of SRI) was introduced to

choose the critical value in this study. It is noted that the number of Black-Spots

identified depends on the standardised scores associated with the Safety Risk Index.

It is strongly suggested that this study can be extended to include costs estimated in

implementing safety intervention activities.

In response to safety concerns at grade crossings, a partnership of railway and

highway authorities would establish various safety management initiatives to reduce

grade crossing collisions. Railway-highway grade crossing collisions tend to be

spread over a vast number of sites, with few (if any) occurring at any given site in

any given year. To improve safety at all grade crossings, a uniform standard would

be prohibitively expensive and impractical. Accordingly, any comprehensive safety

program must begin by first identifying crossings where the risk of collision is

unacceptably high, and where safety countermeasures are most warranted. Following

established convention, these high risk crossings are referred as Black-spots. Since

the SRI targets locations where risk is highest, it is suggested that Black-spot

screening methods would result in the best allocation of scarce safety budgets.

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369

Appendix 1

All Variables in USDOT FRA Databases

Table A1-1: All Variables (152) Recorded in USDOT FRA Inventory Database

NAME OF VARIABLES AS IN THE

DATABASE

DESCRIPTION OF VARIABLES AS IN THE DATABASE

PERCENTAGE OF RECORDS AVAILABLE IN

THE DATABASE

STATUS OF VARIABLE

SELECTION IN MODELLING

REASON FOR EXCLUSION

FROM MODELLING*

CROSSING Crossing ID No 100.0 Yes V

POSXING Position of Crossing 100.0 Yes V

TYPEXING Type of Crossing 100.0 Yes V

WDCODE Warning Device Code 74.8 Yes V

HWYSPEED Posted Highway Speed 100.0 Yes V

MAINTRK Number of Main Tracks 100.0 Yes V

TOTALTRN Total Train = ( DAYTHRU + DAYSWT + NGHTTHRU + NGHTSWT ) 100.0 Yes V

MAXTTSPD Maximum Timetable Speed 100.0 Yes V

XANGLE Smallest Crossing Angle 56.5 Yes V

AADT Annual Average Daily Traffic 56.4 Yes V

TRAFICLN No. of Traffic Lanes Crossing 56.3 Yes V

DOTACPD DOT Accident Prediction Value 100.0 No R

ACCCNT1 Accident history – current complete year 100.0 No R

ACCCNT2 Accident history – prior year 100.0 No R

ACCCNT3 Accident history – two years prior 100.0 No R

ACCCNT4 Accident history – three years prior 100.0 No R

ACCCNT5 Accident history – four years prior 100.0 No R

DOTCASPD DOT Predicted Casualty Rate 100.0 No R

DOTFATPD DOT Predicted Fatality Rate 100.0 No R

SCHLBUS Avg. No of School Buses Passing Over the Crossing on a School Day 100.0 No R

DAYTHRU Day Thru Train Movements 100.0 No R

DAYSWT Switching 100.0 No R

NGHTTHRU Night Thru Train Movements 100.0 No R

NGHTSWT Night Switching Movements 100.0 No R

PASSCNT Avg Passenger Train Count Per Day 100.0 No R

TOTALSWT Total Switching Trains 100.0 No R

MINSPD From Min: 100.0 No R

MAXSPD To Max: 100.0 No R

XBUCKRF Crossbucks-Reflectorized 100.0 No R

XBUCKNRF Crossbucks- Non-reflectorized 100.0 No R

STOPSTD Highway Stop Signs 100.0 No R

STOPOTH Other Stop Sign 100.0 No R

OTHSGN1 Other Signs 100.0 No R

OTHSGN2 Other Signs 100.0 No R

GATERW Gates-Red & White 100.0 No R

GATEOTH Gates-Other 100.0 No R

FLASHOV Canti-levered (or bridged) Flashing Lights-Over Traffic Lane 100.0 No R

FLASHNOV Canti-levered (or bridged) Flashing Lights-Not Over Traffic 100.0 No R

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Table A1-1: All Variables (152) Recorded in USDOT FRA Inventory Database (Contd)

NAME OF VARIABLES AS IN THE

DATABASE

DESCRIPTION OF VARIABLES AS IN THE DATABASE

PERCENTAGE OF RECORDS AVAILABLE IN

THE DATABASE

STATUS OF VARIABLE

SELECTION IN MODELLING

REASON FOR EXCLUSION

FROM MODELLING*

FLASHMAS Mast Mounted Flashing Lights 100.0 No R

FLASHOTH Other Flashing Lights 100.0 No R

HWYSGNL Hwy. Traffic. Signals 100.0 No R

WIGWAGS Wigwags 100.0 No R

BELLS Bells 100.0 No R

XBUCK Crossbucks 100.0 No R

GATES Gates 100.0 No R

FLASHPAI Number of flashing light pairs 100.0 No R

NOSIGNS No Signs or Signals 72.8 No R

SPSEL Train Detection 59.5 No R

ADVWARN RR Advance Warning Signs 56.8 No R

PCTTRUK Estimate Percent Trucks 55.9 No R

HIGHWAY Highway type and No. 48.4 No O

HISTDATE Indicates when ACCCNT1- ACCCNT5 were generated 41.5 No O

ACPDDATE Indicates when DOT ACPD was generated 40.7 No O

PRVIND Private Signs/ Signals 35.9 No O

PRVCAT Private Crossing Category 35.9 No O

LLSOURCE Lat/Long Source 30.5 No O

ENSSIGN ENS Sign 18.8 No O

OTHRTRK Other 17.7 No O

PASSCD Type of Passenger Service 17.4 No O

RRCONT Railroad Contact Telephone Number 13.6 No O

HUMPSIGN Hump Signs 12.9 No O

INTRPRMP Interconnection / Pre-emption 12.9 No O

FOURQUAD Four-quadrant gates present 11.9 No O

ILLUMINA Is Xing Illuminated? 11.9 No O

HWYNRSIG Nearby Intersecting Highway? 11.0 No O

HWYCONT Highway State Contact Telephone Number 10.5 No O

XINGADJ Adjacent Xing with separate no.? 10.3 No O

OTHDES1 Specify 8.6 No O

OTHDES2 Specify 8.6 No O

SAMERR Specify 8.6 No O

PRVSIGN Private Signs-Specify 8.3 No O

XINGOWNR Crossing Owner 8.2 No O

CHANNEL Channelization Devices with Gates 8.2 No O

AADTCALC Not in use (Identify how the AADT was calculated) 4.9 No O

STNARR4 Narrative for State Use 3.0 No O

TRAINCAL Not in use (Identify how the last trains update was calculated) 3.0 No O

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Table A1-1: All Variables (152) Recorded in USDOT FRA Inventory Database (Contd)

NAME OF VARIABLES AS IN THE

DATABASE

DESCRIPTION OF VARIABLES AS IN THE DATABASE

PERCENTAGE OF RECORDS AVAILABLE IN

THE DATABASE

STATUS OF VARIABLE

SELECTION IN MODELLING

REASON FOR EXCLUSION

FROM MODELLING*

STNARR1 Narrative for State Use 2.8 No O

RRMAIN Parent Railroad Code 2.7 No O

TWOQUAD Two-quadrant gates present 2.6 No O

OPENPUB Private Crossing-Public Access 2.5 No O

NARR Narrative 2.4 No O

STNARR3 Narrative for State Use 2.3 No O

STNARR2 Narrative for State Use 2.3 No O

SPECPRO Specify Warning Device: 2.1 No O

OTHRDES Specify 1.8 No O

SEPRR Specify 1.2 No O

FLASHDES Specify 1.1 No O

HSCORRID High Speed Corridor ID Code 0.4 No O

PRVSIGNL Previous Signals -Specify 0.3 No O

XNGADJNO Adjacent Xing with separate no.? 0.3 No O

XSUROTHR Crossing Surface 0.3 No O

WARNACTO Other Train Activated Warning Devices 0.1 No O

RRNARR1 Narrative for Railroad Use 0.1 No O

USERCD Not in use (Refer to field PASSCD) 0.1 No O

RRNARR3 Narrative for Railroad Use 0.1 No O

RRNARR2 Narrative for Railroad Use 0.1 No O

RRNARR4 Narrative for Railroad Use 0.0 No O

RESERVE5 Reserved for Future Use 0.0 No O

RESERVE1 Reserved for Future Use 0.0 No O

FUNCCAT Not in use 0.0 No O

LONGEDAT Same date as EDATE, except that the year in four characters 0.0 No O

RESERVE2 Reserved for Future Use 0.0 No O

RESERVE3 Reserved for Future Use 0.0 No O

RESERVE4 Reserved for Future Use 0.0 No O

LATITUDE Latitude 100.0 No N

LONGITUD Longitude 100.0 No N

EFFDATE Effective Date 100.0 No N

EDATE End Date 100.0 No N

REASON Reason for Update 100.0 No N

BATCH System coded Field 100.0 No N

LONGBDAT Same date as EFFDATE, except that the year in four characters 100.0 No N

STATE State 100.0 No N

CNTYCD County Code 100.0 No N

STATE2 State Code 100.0 No N

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372

Table A1-1: All Variables (152) Recorded in USDOT FRA Inventory Database (Contd)

NAME OF VARIABLES AS IN THE

DATABASE

DESCRIPTION OF VARIABLES AS IN THE DATABASE

PERCENTAGE OF RECORDS AVAILABLE IN

THE DATABASE

STATUS OF VARIABLE

SELECTION IN MODELLING

REASON FOR EXCLUSION

FROM MODELLING*

CITYCD City Code 100.0 No N

RAILROAD Railroad Operating Company 100.0 No N

WHISTBAN New: Whistle Ban (Quiet Zone) 100.0 No N

INIT Initiating Agency 100.0 No N

CNTYNAM County Name 100.0 No N

MILEPOST RR Milepost 100.0 No N

CITYNAM City Name 99.8 No N

UPDATE Not in use (Refer to field UPDATDAT) 99.8 No N

NEAREST In or Near City 99.7 No N

TTSTN Nearest RR Timetable Station 99.5 No N

TTSTNNAM Nearest RR Timetable Station 93.9 No N

RRSUBDIV RR Subdivision 91.4 No N

RRDIV RR Division 90.9 No N

LINK Not in use (Refer to field HSCORRID) 90.4 No N

AADTYEAR Year of the last AADT update 83.8 No N

BRANCH Branch or Line Name 81.4 No N

TRAINDAT Not in use (Year of the last trains update) 80.2 No N

LT1MOV Less Than One Movement Per Day? 74.0 No N

STREET Street or Road Name 69.2 No N

UPDATDAT Date that the last update to the record was posted 68.5 No N

SOURCE Indicate the source of the last update 67.1 No N

POLCONT Emergency Contact Telephone Number Posted at Crossing 62.6 No N

SEPIND Does Another RR Operate a Separate Trk. (Y/N)? 61.1 No N

SAMEIND Does Another RR Operate Over Your Trk. (Y/N)? 60.5 No N

XSURFACE Crossing Surface 59.4 No N

HWYNEAR Nearby Intersecting Highway? 57.7 No N

HWYPVED Is Highway Paved 57.5 No N

TRUCKLN Are Truck Pullout Lanes Present (Y/N)? 57.5 No N

PAVEMRK Pavement Markings 57.5 No N

DOWNST Does Track Run Down a Street 57.5 No N

COMPOWER Commercial Power Available (Y/N)? 57.4 No N

SGNLEQP Signaling for Train Operation: Is Track Equipped with Train Signals 57.4 No N

STHWY1 Is crossing on State Highway System (Y/N)? 56.7 No N

DEVELTYP Type of Development 56.6 No N

HWYSYS Highway System 55.5 No N

HWYCLASS Functional Classification of Road at Crossing 55.3 No N

RRID RR I.D. No. 54.5 No N

MAPREF County Map Ref. No. 52.1 No N

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373

Table A1-2: All Variables (99) Recorded in USDOT FRA Occurrence Database

NAME OF VARIABLES AS IN THE

DATABASE

DESCRIPTION OF VARIABLES AS IN THE DATABASE

PERCENTAGE OF RECORDS AVAILABLE IN

THE DATABASE

STATUS OF VARIABLE

SELECTION IN MODELLING

REASON FOR EXCLUSION

FROM MODELLING*

GXID Grade crossing ID number 100.0 Yes V

YEAR Year of incident 100.0 Yes V

TOTKLD Total killed for railroad as reported 99.8 Yes V

TOTINJ Total injured for railroad as reported 99.8 Yes V

VEHDMG Highway vehicle property damage in $ 99.8 Yes V

TOTOCC Total number in highway vehicle 99.5 Yes V

CASINJRR Number of injured for reporting Railroad calculated 99.8 No R

CASKLDRR Number of killed for reporting RR - calculated 99.8 No R

USERKLD Number of highway-rail crossing users killed 99.8 No R

USERINJ Number of highway-rail crossing users injured 99.7 No R

RREMPKLD Number of railroad employees killed 99.7 No R

RREMPINJ Number of railroad employees injured 99.7 No R

PASSKLD Number of train passengers killed 99.7 No R

PASSINJ Number of train passengers injured 99.7 No R

CROSSING Type of warning device at crossing 99.5 No R

LIGHTS Lights at crossing 99.4 No R

TRNSPD Speed of train in miles per hour 97.3 No R

LOCWARN Location of warning 96.6 No R

DRIVER Highway vehicle driver casualty 96.5 No R

WARNSIG Crossing warning interconnected with highway 95.5 No R

VEHSPD Vehicle estimated speed 93.2 No R

SIGNAL Type of signaled crossing warning 50.2 No R

NARR2 Narrative 30.8 No O

NARR3 Narrative 11.7 No O

HZMMEAS Measure used in hazmat quantity field 8.6 No O

NARR4 Narrative 5.1 No O

HZMQNTY Quantity of hazmat released 5.0 No O

AMTRAK Amtrak involvement 4.9 No O

NARR5 Narrative 2.6 No O

SIGWARNX Further definition of signal field 0.9 No O

HZMNAME Name of hazmat released 0.2 No O

SSB1 Special study block 1 0.1 No O

SSB2 Special study block 2 0.1 No O

DUMMY3 Blank data expansion field 0.0 No O

DUMMY4 Blank data expansion field 0.0 No O

DUMMY5 Blank data expansion field 0.0 No O

MONTH Month of incident 100.0 No N

DAY Day of incident 99.9 No N

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374

Table A1-2: All Variables (99) Recorded in USDOT FRA Occurrence Database (Contd)

NAME OF VARIABLES AS IN THE

DATABASE

DESCRIPTION OF VARIABLES AS IN THE DATABASE

PERCENTAGE OF RECORDS AVAILABLE IN

THE DATABASE

STATUS OF VARIABLE

SELECTION IN MODELLING

REASON FOR EXCLUSION

FROM MODELLING*

TIMEHR Hour of incident 99.9 No N

TIMEMIN Minute of incident 99.9 No N

RAILROAD Railroad code (Reporting RR) 99.9 No N

AMPM am or pm 99.9 No N

RR2 Railroad code (Other RR involved) 99.9 No N

RR3 Railroad code (RR responsible for track maintenance) 99.9 No N

INCDTNO Railroad assigned number 99.9 No N

INCDTNO2 Other Railroad assigned number 99.9 No N

INCDTNO3 RR assigned number 99.9 No N

JOINTCD Indicates railroad reporting 99.9 No N

TYPRR Type of railroad 99.9 No N

DIVISION Railroad division 99.9 No N

DUMMY1 Blank data expansion field 99.8 No N

DUMMY2 Blank data expansion field 99.8 No N

INCDRPT F6180.54 filed 99.8 No N

COUNTY County Name 99.7 No N

STATE FIPS State Code 99.7 No N

REGION FRA designated region 99.7 No N

HIGHWAY Highway name 99.7 No N

CNTYCD FIPS county code 99.7 No N

STCNTY FIPS state and county code 99.7 No N

TYPVEH Type of highway vehicle 99.7 No N

RREQUIP RR equipment involved 99.6 No N

POSITION Position of highway vehicle 99.6 No N

RRCAR Position of car unit in train 99.6 No N

TYPEQ Train equipment involved 99.6 No N

NBRLOCOS Number of locomotive units 99.6 No N

NBRCARS Number of cars 99.6 No N

PLEONTRN Total number of people on train 99.6 No N

TYPSPD Train speed type 99.6 No N

TEMP Temperature in degrees Fahrenheit 99.6 No N

VISIBLTY Visibility 99.6 No N

WEATHER Weather conditions 99.6 No N

STATION Nearest Timetable Station 99.6 No N

VIEW Primary obstruction of track view 99.6 No N

TRNDIR Time table direction 99.6 No N

TYPTRK Type of track 99.5 No N

WHISBAN Whistle ban in effect 99.5 No N

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375

Table A1-2: All Variables (99) Recorded in USDOT FRA Occurrence Database (Contd)

NAME OF VARIABLES AS IN THE

DATABASE

DESCRIPTION OF VARIABLES AS IN THE DATABASE

PERCENTAGE OF RECORDS AVAILABLE IN

THE DATABASE

STATUS OF VARIABLE

SELECTION IN MODELLING

REASON FOR EXCLUSION

FROM MODELLING*

TRKNAME Track identification 99.5 No N

NARRLEN Length of narrative 99.4 No N

TYPACC Circumstance of accident 99.4 No N

HAZARD Entity transporting hazmat 99.4 No N

TRKCLAS FRA track class 99.4 No N

VEHDIR Highway vehicle direction 99.3 No N

MOTORIST Action of motorist 96.4 No N

STANDVEH Motorist passed highway standing vehicle 96.4 No N

INVEH Highway driver in vehicle 96.4 No N

TRAIN2 Motorist struck or was struck by 2nd train 96.4 No N

DRIVGEN Vehicle driver's gender 95.8 No N

HZMRLSED Hazmat released by 93.5 No N

DRIVAGE Vehicle driver's age 84.0 No N

CITY City name 78.5 No N

NARR1 Narrative 58.8 No N

PUBLIC Public crossing 100.0 No D

IYR Year of incident 100.0 No D

IYR2 Year of incident 100.0 No D

IYR3 Year of incident 100.0 No D

IMO Month of incident 100.0 No D

IMO2 Month of incident 99.9 No D

IMO3 Month of incident 99.9 No D

YEAR4 Four digit year of incident 99.9 No D

REASON FOR EXCLUSION OF VARIABLES FROM MODELLING*

V - Variables selected for models

R - Reflection of another variable selected for analysis (partially)

O - Only few records available in the database

N - Not relevant for model prediction

D - Duplication of another variable selected for analysis

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376

Appendix 2

Graphical Distribution of Variables Used

A. Protect ion Type 1 (Crossing w ith No Signs or No signals)

Crossings with No Signs or No Signals

5586 5447

2314 6

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4

Number of Main Tracks

Num

ber

of C

ross

ings

Figure A2-1: Number of Crossings Vs Number of Main Tracks - Protection Type 1

Crossings with No Signs or No Signals

846

1997

8429

0

5000

10000

Between 0 and 29degrees

Between 30 and 59degrees

Between 60 and 90degrees

Track Crossing Angles

Num

ber

of C

ross

ings

Figure A2-2: Number of Crossings Vs Track Crossing Angles - Protection Type 1

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377

Crossings with No Signs or No Signals

6399

1969 1745

545 282 161 61 110 20

2000

4000

6000

8000

1_10

11_2

0

21_3

0

31_4

0

41_5

0

51_6

0

61_7

0

71_8

0

81_9

0

Train Speed (mph)

Num

ber

of C

ross

ings

Figure A2-3: Number of Crossings Vs Train Speed - Protection Type 1

Crossings with No Signs or No Signals

48 253 65 16 33 1

10858

0

4000

8000

12000

1_10

11_2

0

21_3

0

31_4

0

41_5

0

51_6

0

101_

110

Vehicle Speed (mph)

Num

ber

of C

ross

ings

Figure A2-4: Number of Crossings Vs Vehicle Speed - Protection Type 1

Crossings with No Signs or No Signals

386 125 49 42 43 5 6 1 1 1 1

10614

0

4000

8000

12000

0 _10

11 _20

21 _30

31 _40

41 _50

51 _60

61 _70

71 _80

81 _90

151-175

176-200

226-250

Daily Train Movement

Num

ber

of C

ross

ings

Figure A2-5: Number of Crossings Vs Daily Train Movement - Protection Type 1

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378

Crossings with No Signs or No Signals

10239

219 88 83 3642

0

4000

8000

12000

0-5000 10001-15000

15001-20000

20001-40000

40001-60000

5001-10000

Annual Average Daily Traffic ( AADT)

Num

ber

of C

ross

ings

Figure A2-6: Number of Crossings Vs Average Daily Traffic - Protection Type 1

Crossings with No Signs or No Signals

2587

8108

93 4549 18 2 1

0

2000

4000

6000

8000

10000

1 2 3 4 5 6 7 8

Number of Traffic Lanes Crossing Railroad

Num

ber

of C

ross

ings

Figure A2-7: Number of Crossings Vs Number of Traffic Lanes - Protection Type 1

B. Protect ion Type 2 (Crossing w ith Stop Signs or Cros s-bucks)

Crossings with Stop Signs or Crossbucks

17170

96507

3560 61 5 2 20

20000

40000

60000

80000

100000

0 1 2 3 4 5 7

Number of Main Tracks

Num

ber

of C

ross

ings

Figure A2-8: Number of Crossings Vs Number of Main Tracks - Protection Type 2

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379

Crossings with Stop Signs or Crossbucks

4243

20581

92481

0

20000

40000

60000

80000

100000

Between 0 and 29degrees

Between 30 and 59degrees

Between 60 and 90degrees

Track Crossing Angles

Num

ber

of C

ross

ings

Figure A2-9: Number of Crossings Vs Track Crossing Angles - Protection Type 2

Crossings with Stop Signs or Crossbucks

31038

15004

32258

18752

93436602

1850 236594 1

0

5000

10000

15000

20000

25000

30000

35000

1_10

11_2

0

21_3

0

31_4

0

41_5

0

51_6

0

61_7

0

71_8

0

81_9

0

101_

110

Train Speed (mph)

Num

ber

of C

ross

ings

Figure A2-10: Number of Crossings Vs Train Speed - Protection Type 2

Crossings with Stop Signs or Crossbucks

1086 5145 2072 951 3791 7 2

104253

0

40000

80000

120000

1_10

11_2

0

21_3

0

31_4

0

41_5

0

51_6

0

61_7

0

101_

110

Vehicle Speed (mph)

Num

ber

of C

ross

ings

Figure A2-11: Number of Crossings Vs Vehicle Speed - Protection Type 2

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380

Crossings with Stop Signs or Crossbucks

8279 3652 1783 691 496 122 188 109 40 59 14 2 1

101871

0

30000

60000

90000

120000

0 _ 1

0

11 _

20

21 _

30

31 _

40

41 _

50

51 _

60

61 _

70

71 _

80

81 _

90

91 _

100

101_

125

126_

150

151_

175

351_

375

Daily Train Movement

Num

ber

of C

ross

ings

Figure A2-12: Number of Crossings Vs Daily Train Movement - Protection Type 2

Crossings with Stop Signs or Crossbucks

52406

2592 750 279 238 12 2 2 10

20000

40000

60000

0-5000 5001-10000

10001-15000

15001-20000

20001-40000

40001-60000

80001-100000

120001-140000

140001-160000

Annual Average Daily Traffic (AADT)

Num

ber

of C

ross

ings

Figure A2-13: Number of Crossings Vs Average Daily Traffic - Protection Type 2

Crossings with Stop Signs or Crossbucks

24970

89840

356 2015 51 55 9 6 10

20000

40000

60000

80000

100000

1 2 3 4 5 6 7 8 9

Number of Traffic Lanes Crossing Railroad

Num

ber

of C

ross

ings

Figure A2-14: Number of Crossings Vs Number of Traffic Lanes - Protection Type 2

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381

C. Protect ion Type 3 (Crossing w ith Signal s, Bells or Warning Devices)

Crossings with Signals, Bells or Warning Devices

6872

30823

160366 24 6 1 2

0

10000

20000

30000

40000

0 1 2 3 4 5 6 7

Number of Main Tracks

Num

ber

of C

ross

ings

Figure A2-15: Number of Crossings Vs Number of Main Tracks - Protection Type 3

Crossings with Signals, Bells or Warning Devices

1877

7598

29922

0

10000

20000

30000

Between 0 and 29degrees

Between 30 and 59degrees

Between 60 and 90degrees

Track Crossing Angles

Num

ber

of C

ross

ings

Figure A2-16: Number of Crossings Vs Track Crossing Angles - Protection Type 3

Crossings with Signals, Bells or Warning Devices

13408

5761

9237

5186

29741965

338 507 18 2 10

2000

4000

6000

8000

10000

12000

14000

1_10

11_2

0

21_3

0

31_4

0

41_5

0

51_6

0

61_7

0

71_8

0

81_9

0

91_1

00

101_

110

Train Speed (mph)

Num

ber

of C

ross

ings

Figure A2-17: Number of Crossings Vs Train Speed - Protection Type 3

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382

Crossings with Signals, Bells or Warning Devices

2903165

1519 757 1099 29 1

32537

0

10000

20000

30000

40000

1_10

11_2

0

21_3

0

31_4

0

41_5

0

51_6

0

61_7

0

101_

110

Vehicle Speed (mph)

Num

ber

of C

ross

ings

Figure A2-18: Number of Crossings Vs Vehicle Speed - Protection Type 3

Crossings with Signals, Bells or Warning Devices

37291

1733194 102 47 26 2 1 1

0

10000

20000

30000

40000

0-25 26-50 51-75 76-100 101-125 126-150 151-175 176-200 376-400

Daily Train Movement

Num

ber

of C

ross

ings

Figure A2-19: Number of Crossings Vs Daily Train Movement - Protection Type 3

Crossings with Signals, Bells or Warning Devices

38340

955 69 13 1 3 4 2 3 2 3 1 10

10000

20000

30000

40000

0-20

000

2000

1-40

000

4000

1-60

000

6000

1-80

000

8000

1-10

0000

1000

01-1

2000

0

1200

01-1

4000

0

1400

01-1

6000

0

1600

01-1

8000

0

2000

01-2

2000

0

2200

01-2

4000

0

2600

01-2

8000

0

3000

01-3

2000

0

Annual Average Daily Traffic (AADT)

Num

ber

of C

ross

ings

Figure A2-20: Number of Crossings Vs Average Daily Traffic - Protection Type 3

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383

Crossings with Signals, Bells or Warning Devices

1357

32632

6883997

375 255 41 34 120

10000

20000

30000

40000

1 2 3 4 5 6 7 8 9

Number of Traffic Lanes Crossing Railroad

Num

ber

of C

ross

ings

Figure A2-21: Number of Crossings Vs Number of Traffic Lanes - Protection Type 3

D. Protect ion Type 4 (Crossing w ith Gates or Full Barr ier)

Crossings with Gates or Full Barriers

1388

31833

8309

393 66 4 1 30

10000

20000

30000

40000

0 1 2 3 4 5 6 7

Number of Main Tracks

Num

ber

of C

ross

ings

Figure A2-22: Number of Crossings Vs Number of Main Tracks - Protection Type 4

Crossings with Gates or Full Barriers

1350

6005

34640

0

10000

20000

30000

40000

Between 0 and 29degrees

Between 30 and 59degrees

Between 60 and 90degrees

Track Crossing Angles

Num

ber

of C

ross

ings

Figure A2-23: Number of Crossings Vs Track Crossing Angles - Protection Type 4

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384

Crossings with Gates or Full Barriers

3655 3841

63266786

64447011

3476

4315

135 3 50

2000

4000

6000

8000

1_10

11_2

0

21_3

0

31_4

0

41_5

0

51_6

0

61_7

0

71_8

0

81_9

0

91_1

00

101_

110

Train Speed (mph)

Num

ber

of C

ross

ings

Figure A2-24: Number of Crossings Vs Train Speed - Protection Type 4

Crossings with Gates or Full Barriers

425

43892308 963 1560

34 2

32316

0

10000

20000

30000

40000

1_10

11_2

0

21_3

0

31_4

0

41_5

0

51_6

0

61_7

0

71_8

0

Vehicle Speed (mph)

Num

ber

of C

ross

ings

Figure A2-25: Number of Crossings Vs Vehicle Speed - Protection Type 4

Crossings with Gates or Full Barriers

30164

8498

2026 988 167 71 49 30 1 1 20

10000

20000

30000

40000

0-25 26-50 51-75 76-100

101-125

126-150

151-175

176-200

201-225

251-275

376-400

Daily Train Movement

Num

ber

of C

ross

ings

Figure A2-26: Number of Crossings Vs Daily Train Movement - Protection Type 4

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385

Crossings with Gates or Full Barriers

1209 111 16 9 3 7 7 2 6 2 4 2

40619

0

10000

20000

30000

40000

50000

0-20

000

2000

1-40

000

4000

1-60

000

6000

1-80

000

8000

1-10

0000

1000

01-1

2000

0

1200

01-1

4000

0

1600

01-1

8000

0

1800

01-2

0000

0

2000

01-2

2000

0

2600

01-2

8000

0

2800

01-3

0000

0

3000

01-3

2000

0

Annual Average Daily Traffic (AADT)

Num

ber

of C

ross

ings

Figure A2-27: Number of Crossings Vs Average Daily Traffic - Protection Type 4

Crossings with Gates or Full Barriers

1261

34760

787

4284

477 339 52 30 60

10000

20000

30000

40000

1 2 3 4 5 6 7 8 9

Number of Traffic Lanes Crossing Railroad

Num

ber

of C

ross

ings

Figure A2-28: Number of Crossings Vs Number of Traffic Lanes - Protection Type 4

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386

Appendix 3

Descriptive Statistics on Model Variables

A. Protect ion Type 1 (Crossing w ith No Signs or No signals)

Table A3-1: Descriptive Statistics on Variables used in Accident Prediction Model

Variable N Minimum Maximum Mean Std. Deviation

Number of Accidents in 5 Years 11273 0 4 0.01 0.1

Daily Train Movement 11273 1 241 3.36 7.23

Annual Average Daily Traffic 11273 1 46782 1541.4 3336.05

Track Crossing Angle 11273 1 3 2.90 0.58

Maximum Timetable Train Speed 11273 1 90 16.92 13.57

Highway Speed 11273 0 55 1.13 6.04

Number of Main Tracks 11273 0 4 0.53 0.55

Number of Traffic Lanes 11273 0 8 1.87 0.65

Table A3-2 Descriptive Statistics on Variables used in Consequence Prediction Model

Variable N Minimum Maximum Mean Std. Deviation

Number of Accidents in 5 Years 84 1 4 1.08 0.42

Number of Fatalities in 5 Years 84 0 1 0.01 0.11

Number of injuries in 5 Years 84 0 2 0.21 0.49

Vehicle property damage ($) in 5 Years 84 0 80,000 3,800.60 9,559.87

B. Protect ion Type 2 (Crossing w i th Stop Signs or Cross-bucks)

Table A3-3 Descriptive Statistics on Variables used in Accident Prediction Model

Variable N Minimum Maximum Mean Std. Deviation

Number of Accidents in 5 Years 117304 0 15 0.04 0.24

Daily Train Movement 117304 1 364 5.52 9.64

Annual Average Daily Traffic 117304 1 150550 763.08 2287.5

Track Crossing Angle 117304 1 3 2.81 0.45

Maximum Timetable Train Speed 117304 1 110 28.13 17.32

Highway Speed 117304 0 70 4.14 12.49

Number of Main Tracks 117304 0 7 0.89 0.41

Number of Traffic Lanes 117304 0 9 1.85 0.5

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387

Table A3-4 Descriptive Statistics on Variables used in Consequence Prediction Model

Variable N Minimum Maximum Mean Std. Deviation

Number of Accidents in 5 Years 3998 1 15 1.19 0.56

Number of Fatalities in 5 Years 3998 0 5 0.11 0.39

Number of injuries in 5 Years 3998 0 35 0.39 0.88

Vehicle property damage ($) in 5 Years 3998 0 250,000 5,531.00 12,484.17

C. Protect ion Type 3 (Crossing w ith Signals, Bells or Warning Devices)

Table A3-5 Descriptive Statistics on Variables used in Accident Prediction Model

Variable N Minimum Maximum Mean Std. Deviation

Number of Accidents in 5 Years 39394 0 12 0.07 0.34

Daily Train Movement 39394 1 180 6.75 11.04

Annual Average Daily Traffic 39394 1 267240 3989.2 6871.33

Track Crossing Angle 39394 1 3 2.78 0.49

Maximum Timetable Train Speed 39394 0 110 25.28 16.77

Highway Speed 39394 0 70 6.21 14.29

Number of Main Tracks 39394 0 7 0.87 0.46

Number of Traffic Lanes 39394 0 9 2.25 0.81

Table A3-6 Descriptive Statistics on Variables used in Consequence Prediction Model

Variable N Minimum Maximum Mean Std. Deviation

Number of Accidents in 5 Years 2130 1 12 1.28 0.75

Number of Fatalities in 5 Years 2130 0 5 0.09 0.38

Number of injuries in 5 Years 2130 0 6 0.33 0.65

Vehicle property damage ($) in 5 Years 2130 0 500,000 4,354.95 13,664.02

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388

D. Protect ion Type 4 (Crossing w ith Gates or Full B arrier)

Table A3-7 Descriptive Statistics on Variables used in Accident Prediction Model

Variable N Minimum Maximum Mean Std. Deviation

Number of Accidents in 5 Years 41994 0 8 0.13 0.44

Daily Train Movement 41994 1 255 20.29 21.26

Annual Average Daily Traffic 41994 1 308060 4272.3 8532.07

Track Crossing Angle 41994 1 3 2.84 0.51

Maximum Timetable Train Speed 41994 1 110 44.28 20.92

Highway Speed 41994 0 80 8.19 15.85

Number of Main Tracks 41994 0 7 1.19 0.5

Number of Traffic Lanes 41994 0 9 2.27 0.82

Table A3-8 Descriptive Statistics on Variables used in Consequence Prediction Model

Variable N Minimum Maximum Mean Std. Deviation

Number of Accidents in 5 Years 4298 1 8 1.27 0.69

Number of Fatalities in 5 Years 4298 0 5 0.17 0.45

Number of injuries in 5 Years 4298 0 28 0.33 0.92

Vehicle property damage ($) in 5 Years 4298 0 200,000 4,878.08 11,235.48

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389

Appendix 4

List of Publications

Samaranayake, P., Matawie, K.M. and Rajayogan, R. 2011, “Evaluation of Safety

Risks at Railway Grade Crossings: Conceptual Framework Development”, Refereed

Paper, ICQR 2011, Bangkok, Thailand.

Rajayogan, R. and Jayaraman, V. 2004, “Assessing and Prioritising Noise Hazard

Potentials at Workplaces Using Workers Compensation Statistics”, Refereed Paper,

ANZAM 2004, University of Otago, Dunedin, New Zealand.


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