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
ii
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)
iii
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
iv
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.
v
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
xiv
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
xvii
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.
1
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
2
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;
3
• 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.
4
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
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.
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
6
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
7
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.
8
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
9
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)
10
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:
11
• 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
12
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
13
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.
14
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.
15
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
16
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.
17
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
18
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.
19
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
20
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
21
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
22
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)
23
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.
24
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;
25
• 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
26
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.
27
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:
28
• 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.
29
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
30
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.
31
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
32
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).
33
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
38
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
39
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
48
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
71
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
72
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
74
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
77
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
80
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
81
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
500
1000
1500
2000
2500
3000
3500
Portu
gal
Belgiu
m
Nethe
rland
s
New Z
eala
nd
Canad
a
Germ
any
Japa
n
Luxe
mbour
gUSA
Finlan
d
Franc
e
Austra
lia
Grea
t Brit
ain
Sweden
Irelan
d
Country
Ann
ual A
vera
ge o
f C
ollis
ions
0.00000.00500.01000.01500.02000.02500.03000.03500.04000.0450
Ann
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ollis
ions
per
Le
vel C
ross
ing
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
Nether
lands
Portug
al
Belgium
New Z
ealan
dJa
pan
Austra
lia
Luxe
mbour
g
Germ
any
Canad
a
Franc
e
Finlan
dUSA
Great B
ritain
Sweden
Irelan
d
Country
Ann
ual A
vera
ge o
f F
atal
ities
0.00000.00100.00200.00300.00400.00500.00600.00700.00800.00900.0100
Ann
ual F
atal
ities
per
Lev
el
Cro
ssin
g
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
108
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
111
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
112
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.
114
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
115
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.
116
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.
117
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
118
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,
119
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).
120
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
121
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
122
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):
123
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
124
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.
125
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:
126
(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)
127
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
128
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
129
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:
130
)/()(
)()( 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
131
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
132
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
133
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
134
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.
135
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
136
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
137
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
138
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
139
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).
140
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
141
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.
142
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
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.
144
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].
145
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.
146
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
147
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
148
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
149
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.
150
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.
151
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.
152
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.
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
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
155
(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.
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.
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.
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.
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
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
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)
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).
163
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)
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.
165
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
166
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
167
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.
168
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
169
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
170
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,
171
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)
172
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.
173
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
174
(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
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
176
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
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)
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)
179
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)
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)
181
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.
182
(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
183
(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
184
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
185
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:
186
∑== +=
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
187
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
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
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 ).
190
)(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)
191
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:
192
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”,
193
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 &
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
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.
196
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
197
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)
198
= )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
199
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
200
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).
201
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.
202
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
203
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.
204
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)
205
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)
206
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)
207
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)
208
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.
209
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)
210
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.
211
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.
212
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.
213
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
214
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:
215
(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
216
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.
217
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.
218
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
219
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.
220
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:
221
(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.
222
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.
223
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
224
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
225
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
226
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.
227
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.
228
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.
229
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.
230
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
231
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.
232
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
233
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
234
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.
235
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
236
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.
237
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:
238
(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.
239
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
240
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
241
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
242
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’.
243
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
244
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
245
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
246
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
247
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.
248
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.
249
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
250
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.
251
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
252
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
253
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.
254
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
255
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.
256
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.
257
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
258
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.
259
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:
260
=+= 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.
261
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.
262
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.
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:
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
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.
266
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:
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.
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
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.
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:
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
272
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.
273
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:
274
=+= 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
275
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.
276
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.
277
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:
278
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
279
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’
280
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
281
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
282
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).
283
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
284
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.
285
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
286
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
287
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).
288
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
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
290
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
291
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
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
293
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
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
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
296
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
297
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
298
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
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
300
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
301
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
302
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
303
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
304
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.
305
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).
306
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
307
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.
308
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:
309
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.
310
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
311
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
312
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
313
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
314
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,
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
316
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.
317
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.
318
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
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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
320
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
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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
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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
322
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
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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
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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
324
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
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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.
330
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.
331
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
332
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.
333
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.
334
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
335
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
337
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;
338
• 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.
339
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
340
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:
341
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
342
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
344
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.
345
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
346
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
347
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
348
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
349
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.
350
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
351
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
352
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.
353
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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
370
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
371
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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 ($) in 5 Years 84 0 80,000 3,800.60 9,559.87
B. Protect ion Type 2 (Crossing w i th Stop Signs or Cross-bucks)
Table A3-3 Descriptive Statistics on Variables used in Accident Prediction Model
Variable N Minimum Maximum Mean Std. Deviation
Number of Accidents in 5 Years 117304 0 15 0.04 0.24
Daily Train Movement 117304 1 364 5.52 9.64
Annual Average Daily Traffic 117304 1 150550 763.08 2287.5
Track Crossing Angle 117304 1 3 2.81 0.45
Maximum Timetable Train Speed 117304 1 110 28.13 17.32
Highway Speed 117304 0 70 4.14 12.49
Number of Main Tracks 117304 0 7 0.89 0.41
Number of Traffic Lanes 117304 0 9 1.85 0.5
387
Table A3-4 Descriptive Statistics on Variables used in Consequence Prediction Model
Variable N Minimum Maximum Mean Std. Deviation
Number of Accidents in 5 Years 3998 1 15 1.19 0.56
Number of Fatalities in 5 Years 3998 0 5 0.11 0.39
Number of injuries in 5 Years 3998 0 35 0.39 0.88
Vehicle property damage ($) 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 ($) in 5 Years 2130 0 500,000 4,354.95 13,664.02
388
D. Protect ion Type 4 (Crossing w ith Gates or Full B arrier)
Table A3-7 Descriptive Statistics on Variables used in Accident Prediction Model
Variable N Minimum Maximum Mean Std. Deviation
Number of Accidents in 5 Years 41994 0 8 0.13 0.44
Daily Train Movement 41994 1 255 20.29 21.26
Annual Average Daily Traffic 41994 1 308060 4272.3 8532.07
Track Crossing Angle 41994 1 3 2.84 0.51
Maximum Timetable Train Speed 41994 1 110 44.28 20.92
Highway Speed 41994 0 80 8.19 15.85
Number of Main Tracks 41994 0 7 1.19 0.5
Number of Traffic Lanes 41994 0 9 2.27 0.82
Table A3-8 Descriptive Statistics on Variables used in Consequence Prediction Model
Variable N Minimum Maximum Mean Std. Deviation
Number of Accidents in 5 Years 4298 1 8 1.27 0.69
Number of Fatalities in 5 Years 4298 0 5 0.17 0.45
Number of injuries in 5 Years 4298 0 28 0.33 0.92
Vehicle property damage ($) in 5 Years 4298 0 200,000 4,878.08 11,235.48
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.