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RELIABILITY AND RISK ANALYSIS

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ELSEVIER SCIENCE PUBLISHERS LTDCrown House, Linton Road, Barking, Essex IGl18JU England

WITH 17 TABLES AND 65 ILLUSTRATIONS

© 1992 ELSEVIER SCIENCE PUBLISHERS LTD

British Library Cataloguing in Publication Data

Aven, T.Reliability and Risk AnalysisI Title620

ISBN 1-85166-896-9

Library of Congress CIP data applied for

No responsibility is assumed by the Publisher for any injury and/or damage to persons orproperty as a matter of products liability, negligence or otherwise, or from any use or operation

of any methods, products, inst ructions or ideas contained in the material herein.

Special regulations for readers in the USAThis publication has been registered with the Copyright Clearance Center Inc. CCC), Salem,Massachusetts. Information can be obtained from the CCC about conditions under whichphotocopies of parts of this publication may be made in the USA. All other copyright questions,

including photocopying outside the USA, should be referred to the publisher.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system,or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, orotherwise, without the prior written permission of the publisher.

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Preface

Analysis of reliability and risk is an important and integral part of planning, constructionand operation of all technical systems. To be able to perform such analyses systematicallyand scientifically, there is usually a need for special methods and models. This bookpresents the most important of these. Part icular emphasis has been placed on the ideasand the motivation for the use of the various methods and models. It has been an objectiveto compile a book which provides practising engineers and engineering graduates with theconcepts and basic techniques for evaluating reliability and risk. I t is hoped that thematerial presented will make them so familiar with the subject that they can carry outvarious types of analyses themselves and understand and make use of the more detailedapplications and additional material which is available in the journals and publications

associated with their own discipline. It has also been an objective to put reliability andrisk analyses in context - how such analyses should be used in design and operation ofcomponents and systems.

The material presented is modern and a large part of the book is at research level.The book focuses on analysis of repairable systems, not only non-repairable systems whichhave traditionally been given most attent ion in textbooks on reliability theory. Since mostreal-life systems are repairable, methods for analysing repairable systems are an importantarea of research.

The book presents general methods, with most applications taken from offshore petroleum activities.

Reliability and risk analysis comprises a large number of fields and application areas.I t has not been the purpose of this book to give a total overview of all these fields andapplication areas. This book does not, for example, cover structural reliability and softwarereliability.

What topics are covered in this book? Chapter 1 introduces some important conceptsand gives a general description of a reliability analysis and a risk analysis. In Chapter 2some basic reliability and risk analysis methods are presented. These include Failure modeand effect analysis, Fault tree analysis, Event tree analysis and Cause consequence analysis.Chapter 3 presents the most common techniques for calculating system reliability. Models

for analysing periodically tested systems, and systems where the components are repairedor replaced at failure are studied. Methods for identification of critical components andevents are also discussed. Chapter 4 studies multis tate models where the components andthe system are allowed to have an arbitrary number of states, not only two as in the traditional models described in Chapter 3. Analysis of flow network systems is emphasized.Such networks can be used to model e.g. gas and oil production and transportation systerm. Chapter 5 reviews some common models for optimizing the limiting availability,or more generally the long run expected cost per time unit, when the system is undergoing preventive maintenance. The problem is to find the optimal replacement time of thesystem. Chapter 6 presents an overview of the most important elements of safety man-

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VI

agement. By safety management is understood all actions taken to obtain and maintain asafety level in accordance with goals and criteria. Emphasis is put on describing the roleof reliability and risk analysis as a part of safety management. Chapter 7 presents someapplications of reliability and risk analysis. The examples are taken from the petroleumactivity in the North Sea.

Chapters 1, 2, 6 and part of Chapter 7 can be read without background in probabilitytheory and statistics. Chapters 3, 4, 5 and part of Chapter 7 assume, however, a knowledgeof elementary probability theory and some basic concepts such as failure rate, lifetimedistribution, etc. Appendices A and B present a short overview of this material.

A reliability analysis and a risk analysis usually requires a statistical analysis of reliability data to estimate lifetime distributions, repair time distributions, mean lifetimes,etc. Appendix C describes how such analyses can be carried out. In Appendix D Markovmodels are studied. Markov models are used to establish some of the results obtained in

Chapter 3. Appendix E presents some more advanced parts of the theory of stochasticprocesses, including renewal theory, renewal reward theory and counting processes. Thistheory is needed to prove some results in Chapters 3 and 5.

A number of examples and exercises have been included to illustrate, clarify, and supplement the theory and methods.

This book is based on a Norwegian version with the same title, issued in 1991 [8]. Thepresent version is, however, more advanced and includes many parts that are not coveredin the original [8].

The Norwegian version of the book originated from a course in Reliability and RiskAnalysis at Rogaland University Centre, Stavanger. The Norwegian version is also used in

safety education at the University of Oslo and at the University of Trondheim, NorwegianInstitute of Technology.

Parts of the Norwegian book were written when I was working in Statoil, the NorwegianState Oil Company. I would like to thank Hans J. Grundt and Jo Hulbrekdal in Statoi l formany valuable suggestions and comments.

Stavanger

Terje Aven

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Contents

Preface v

1 INTRODUCTION TO RELIABILITY AND RISK ANALYSIS 11.1 Historical perspective. . . . . . . . . . . 11.2 Objectives of reliability and risk analyses 21.3 Subject areas. Modelling . . . . . 31.4 Basic concepts. . . . . . . . . . . 4

1.4.1 Probability and frequency 51.4.2 Accidents and near misses 51.4.3 R e l i a b i l i t y 51.4.4 Reliability analysis . . . 61.4.5 Reliability management 61.4.6 Risk . . . . . 61.4.7 Risk analysis 101.4.8 Safety . . . . . . . 10

1.4.9 Safety management 101.4.10 Acceptance criteria 101.5 Planning, execution and use of reliability analysis 13

1.5.1 Planning of reliability analysis . 131.5.2 Execution of reliability analysis . . . 151.5.3 Use of reliability analysis. . . . . . . 16

1.6 Planning, execution and use of risk analysis 171.7 Discussion 201.8 P r o b l e m s 22

2 BASIC RELIABILITYAND

RISK ANALYSIS METHODS5

2.1 Use of statistics . . . 252.1.1 Accident data . 262.1.2 Near misses . . 322.1.3 Reliability data 32

2.2 Failure mode and effect analysis 352.2.1 I n t r o d u c t i o n 352.2.2 Basic principles for FMEA 35

Vll

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2.2.3 Execution of an FMEA .2.2.4 Resources .2.2.5 Example 2.3: Storage tank .2.2.6 Discussion

2.3 Fault tree analysis2.3.1 Introduction.

2.3.2 Description of a fault tree2.3.3 Definition of undesirable events and framework conditions2.3.42.3.52.3.62.3.72.3.8

Fault tree construction .Minimal cut sets .Qualit ative analysis of the fault tree .Quantitative analysis of the fault t ree.Resources .

2.3.9 Discussion .2.4 Cause consequence analysis/Event tree analysis

2.4.1 Introduction .2.4.2 CCA diagram .2.4.32.4.42.4.52.4.6

Definition of initiating events and framework conditions.Construction of the CCA diagramQualitative analysis of the CC diagram .Quantitative analysis of the CCA diagram

2.4.7 Resources .2.4.8 Discussion .

2 5 Other reliability and risk analysis methods .2.5.1 Coarse risk analysis/Preliminary risk analysis2.5.2 Hazard and operability studies .2.5.3 Other analysis methods .2 .5.4 Special methods for analysing human reliability

2.6 Problems .

CONTENTS

35393940444445484852525455

55565657576061616666

686871

748082

3 BINARY MODELS FOR ANALYSING SYSTEM RELIABILITY 873.1 Structural properties . . . . . . . . . . . . 873.2 Computing system reliabi lity. . . . . . . . . . . . 91

3.2.l Computing exact system reliability . . . . 923.2.2 Computing approximate system reliability 96

3.:3 Non-repairable systems. . . . . . . . . 973.4 Repairable systems . . . . . . . . . . . 99

3.4.1 Replacement/repair at failures. 993.4.2 Preventive maintenance policy. 1023.4.3 A model for analysing standby systems 1043.4.4 Periodical testing/replacement. 108

3.5 Reliability importance measures 1133.5.1 Improvement potential . . . . . 113

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CONTENTS

3.5.2 Birnbaum s measure .3.5.3 Some comments on the use of importance measures

3.6 Dependent components .

3.6.1 Analysing dependent components (common-mode failures)3.7 Problems .

4 MULTISTATE MODELS FOR ANALYSING SYSTEMRELIABILITY4.1 Multistate monotone systems4.2 Computing system reliabi lity.4.3 A time dependent model . . .

4.3.1 Performance measures4.3.2 Computation of the performance measures

4.3.3 Including deferrable repairs4.4 Discussion4.5 P r o b l e m s

5 OPTIMAL REPLACEMENT POLICIES5.1 Introduction .5.2 General minimal repair, age replacement model

5.2.1 The optimization problem5.2.2 An extension .

5.3 Block replacement model .5.4 On-condition replacement models5.5 Problems .

6 SAFETY MANAGEMENT6.1 Introduction .

IX

114115116

118120

125125127131132133

140144145

49

149151151153154155161

63

1636.2 Safety management in a company . . . . . . . 165

6.2.1 Policies, goals and acceptance criteria. 1656.2.2 Alternative solutions . . . . . . . . . . 1696.2.3 A n a l y s i s 180

6.2.4 Evaluation of results, actions/choice of solution 1806.2.5 Safety management in different phases 1826.2.6 Examples of safety programmes 185

6.3 Reliability management of a product 1966.3.1 Policies, goals and cri teria 1966.3.2 Alternative solutions . . . . . 1976.3.3 Analysis and testing . . . 1996.3.4 Evaluation of results, actions/choice of solution 2006.3.5 Reliability programme - Reliability management in different phases 200

6.4 P r o b l e m s 203

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7 SOME APPLICATIONS 2 5205205

206206208208209209218219221

7.1 Risk analysis of an offshore oil and gas producing platform7.1.1 Objectives of the analysis7.1.2 Study approach7.1.3 Risk7.1.47.1.57.1.67.1.77.1.87.1.97.1.10

UncertaintyAssumptions. .Identification of undesirable eventsProcess leaks, fire and explosionOccupational riskRisk picture . . . . . . . . . . .Risk evaluation . . . . . . . . .

7.1.11 Risk factors and risk reducing measures. 224

7.1.12 Foilow-up . . . . . . . . . . . . . . . . . 2267.2 Availability and life cycle costing in a gas project 228

7.2.1 Approach . . . 2287.2.2 Cost elements . . . 2297.2.3 Reliability data . . 2307.2.4 Economic analysis 2317.2.5 E x a m p l e 232

7.3 Availability and life cycle costing related to a process instrumentationsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2347.3.1 Approach . 235

7.3.2 C o n c l u s i o n 2377.4 D i s c u s s i o n 237

7.4.1 Concept Safety Evaluation. 2377.4.2 Safety management in general 2397.4.3 Risk acceptance criteria 242

7.5 Problems 248

APPENDICIES

A PROBABILITY THEORY 249

A.1 Probabilities. . . . . . . . . . . . . . . . 249A.1.1 Probability concepts . . . . . 249A.1.2 Rules for combining probabilities 250A.1.3 Conditional probabilities 253A.1.4 Independence 254

A.2 Stochastic variables . . . . . . 255A.3 Some proofs . . . . . . . . . . 257

A.3.1 Proof of formula (A.4) 257A.3.2 Probability calculations in event trees. 258A.3.3 Proof of an error bound for the approximations (4.2) and (4.3) 259

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CONTENTS

A.4 Problems. . . . . . . . . . . . . . . .

B STOCHASTIC FAILURE MODELSB 1 Non-repairable units .

B.l.1 Basic concepts .B.l.2 Some common lifetime dis tribut ions.

B.2 Repairable unitsB.3 Binomial distributionB.4 Gamma functionB.5 Problems .

C STATISTICAL ANALYSIS OF RELIABILITY DATAC.1 Identification of lifetime distribution, Hazard plotting . .C.2 Estimation of parameters in lifetime distributionsC.3 Statistical analysis of non-homogeneous Poisson processes.C.4 Data sources.C.5 Problems. . . . . .

D MARKOV MODELSD.1 Introduction .D.2 One component. No repair .D.3 One repairable component .D.4 Two repairable componentsD.5 Birth and death processes .D.6 General formulation of a Markov processD.7 Problems .

E MORE ON STOCHASTIC PROCESSESE.1 Renewal processes. . . . .E.2 Renewal reward processesE.3 Regenerative processesE.4 Counting processes . . . .E.5 Proofs of some results in Chapters 3 and 5

E.5.1 Section 3.4.1 .E.5.2 Section 3.4.2 .E.5.3 Section 5.4

Xl

260

263263263267271273274276

277277282287292293

295295296298300303304306

3 9309311312313315315318320

F AN ALGORITHM FOR CALCULATING SYSTEM RELIABILITY 323

G A MINIMIZATION TECHNIQUE 329

BIBLIOGRAPHY 333

INDEX 343

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