System Reliability Theory: Models and Statistical Methods (Wiley Series in Probability and Mathematical Statistics. Applied Probability and Statisti)

644 Pages·1994·24.66 MB·English

by  Arnljot Hoyland

SYSTEM RELIABILITY
THEORY
Second Edition
WILEY SERIES IN PROBABILITY AND STATISTICS
Established by WALTER A. SHEWHART and SAMUEL S. WILKS
Editors: David J Balding, Noel A. C. Cressie. Nicholas I. Fishel;
Iain M. Johnstone, 1 B. Kadane, Geert Molenberghs, Louise M. Ryan,
David U? Scott, Adrian l? M. Smith, Jozef L. Teugels
Editors Emeriti: Vic Barnett, .lS tuart Hunter: David G. Kendall
A complete list of the titles in this series appears at the end of this volume.
SYSTEM RELIABILITY
THEORY
Models, Statistical Methods,
and Applications
SECOND EDITION
Marvin Rausand
,!?Cole des Mines de Nantes
Departement Productique et Automatique
Nantes Cedex 3 France
Arnljot Hsyland
@EKicIENCE
A JOHN WILEY & SONS, INC., PUBLICATION
Copyright 0 2004 by John Wiley & Sons, Inc. All rights reserved.
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Published simultaneously in Canada.
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Library of Congress Cataloging-in-Publication Data:
Rausand, Marvin.
System reliability theory : models, statistical methods, and applications / Marvin
Rausand, Arnljot H~yland-. 2nd ed.
p. cm. - (Wiley series in probability and mathematics. Applied probability and statistics)
Hsyland's name appears first on the earilcr edition.
Includes bibliographical references and index.
ISBN 0-471-47133-X (acid-free paper)
1. Reliability (Engineering)-Statistical methods. I. Hoyland, Arnljot, 1924- 11. Title. 111
Series.
TA169.H68 2004
620'.004526c22 2003057631
Printed in the United States of America
1 0 9 8 7 6 5 4 3 2 1
The second edition is dedicated to the memory of
Professor Arnljot Hayland (1924-2002)
Contents
Preface to the Second Edition xiii
Preface to the First Edition xvii
Acknowledgments xix
1. Introduction 1
1.1 A Brief History, 1
1.2 Different Approaches to Reliability Analysis, 2
1.3 Scope of the Text, 4
1.4 Basic Concepts, 5
1.5 Application Areas, 8
1.6 Models and Uncertainties, 1 1
1.7 Standards and Guidelines, 14
2. Failure Models 15
2.1 Introduction, 15
2.2 State Variable, 16
2.3 Time to Failure, 16
2.4 Reliability Function, 17
2.5 Failure Rate Function, 18
2.6 Mean Time to Failure, 22
2.7 Mean Residual Life, 23
2.8 The Binomial and Geometric Distributions, 25
2.9 The Exponential Distribution, 26
2.10 The Homogeneous Poisson Process, 3 1
2.1 1 The Gamma Distribution, 33
2.12 The Weibull Distribution, 37
2.13 The Normal Distribution, 4 1
2.14 The Lognormal Distribution, 43
2.15 The Birnbaum-Saunders Distribution, 47
2.16 The Inverse Gaussian Distribution, 50
2.17 The Extreme Value Distributions, 54
vii
Viii CONTENTS
2.18 Stressor-Dependent Modeling, 58
2.19 Some Families of Distributions, 59
2.20 Summary of Failure Models, 63
Problems, 65
3. Qualitative System Analysis 73
3.1 Introduction, 73
3.2 Systems and Interfaces, 74
3.3 Functional Analysis, 77
3.4 Failures and Failure Classification, 83
3.5 Failure Modes, Effects, and Criticality Analysis, 88
3.6 Fault Tree Analysis, 96
3.7 Cause and Effect Diagrams, 106
3.8 Bayesian Belief Networks, 107
3.9 Event Tree Analysis, 108
3.10 Reliability Block Diagrams, 1 18
3.1 1 System Structure Analysis, 125
Problems, I39
4. Systems of Independent Components 147
4.1 Introduction, 147
4.2 System Reliability, 148
4.3 Nonrepairable Systems, 153
4.4 Quantitative Fault Tree Analysis, I60
4.5 Exact System Reliability, 166
4.6 Redundancy, 173
Problems, 178
5. Component Importance 183
5.1 Introduction, 183
5.2 Birnbaum's Measure, 185
5.3 Improvement Potential, 189
5.4 Risk Achievement Worth, 190
5.5 Risk Reduction Worth, 19 1
5.6 Criticality Importance, 192
5.7 Fussell-Vesely's Measure, 193
5.8 Examples, I97
Problems, 204
6. Dependent Failures 207
6.1 Introduction, 207
6.2 How to Obtain Reliable Systems, 2 10
6.3 Modeling of Dependent Failures, 2 14
CONTENTS ix
6.5 Associated Variables, 223
Problems, 228
7. Counting Processes 23 1
7.1 Introduction, 23 1
7.2 Homogeneous Poisson Processes, 240
7.3 Renewal Processes, 246
7.4 Nonhomogeneous Poisson Processes, 277
7.5 Imperfect Repair Processes, 287
7.6 Model Selection, 295
Problems, 298
8. Markov Processes 301
8.1 Introduction, 301
8.2 Markov Processes, 303
8.3 Asymptotic Solution, 3 15
8.4 Parallel and Series Structures, 322
8.5 Mean Time to First System Failure, 328
8.6 Systems with Dependent Components, 334
8.7 Standby Systems, 339
8.8 Complex Systems, 346
8.9 Time-Dependent Solution, 35 1
8.10 Semi-Markov Processes, 353
Problems, 355
9. Reliability of Maintained Systems 361
9.1 Introduction, 361
9.2 Types of Maintenance, 363
9.3 Downtime and Downtime Distributions, 364
9.4 Availability, 367
9.5 System Availability Assessment, 373
9.6 Preventive Maintenance Policies, 380
9.7 Maintenance Optimization, 400
Problems, 4 16
10. Reliability of Safety Systems 419
10.1 Introduction, 41 9
10.2 Safety Instrumented Systems, 420
10.3 Probability of Failure on Demand, 426
10.4 Safety Unavailability, 436
10.5 Common Cause Failures, 442
10.6 IEC61508, 446
10.7 The PDS Approach, 452
X CONTENTS
10.7 The PDS Approach, 452
10.8 Markov Approach, 453
Problems, 459
11. Life Data Analysis 465
1 1.1 Introduction, 465
1 1.2 Complete and Censored Data Sets, 466
1 1.3 Nonparametric Methods, 469
1 1.4 Parametric Methods, 500
1 1.5 Model Selection, 5 15
Problems, 5 18
12. Accelerated Life Testing 525
12.1 Introduction, 525
12.2 Experimental Designs for ALT, 526
12.3 Parametric Models Used in ALT, 527
12.4 Nonparametric Models Used in ALT, 535
Problems, 537
13. Bayesian Reliability Analysis 539
13.1 Introduction, 539
13.2 Basic Concepts, 541
13.3 Bayesian Point Estimation, 544
13.4 Credibility Interval, 546
13.5 Choice of Prior Distribution, 547
13.6 Bayesian Life Test Sampling Plans, 553
13.7 Interpretation of the Prior Distribution, 555
13.8 The Predictive Density, 557
Problems, 558
14. Reliability Data Sources 561
14.1 Introduction, 561
14.2 Types of Reliability Databases, 562
14.3 Generic Reliability Databases, 564
14.4 Data Analysis and Data Quality, 569
Appendix A. The Gamma and Beta Functions 573
A. 1 The Gamma Function, 573
A.2 The Beta Function, 574
Appendix B. Laplace Transforms 577
Appendix C. Kronecker Products 581