Marvin Rausand - System Reliability Theory

1 Cover

2 Wiley Series in Probability and Statistics Wiley Series in Probability and Statistics Established by WALTER A. SHEWHART and SAMUEL S. WILKS Editors David J. Balding, Noel A.C. Cressie, Garrett M. Fitzmaurice, Harvey Goldstein, Geert Molenberghs, David W. Scott, Adrian F.M. Smith, and Ruey S. Tsay Editors Emeriti Vic Barnett, Ralph A. Bradley, J. Stuart Hunter, J.B. Kadane, David G. Kendall, and Jozef L. Teugels A complete list of the titles in this series appears at the end of this volume.

3 System Reliability Theory System Reliability Theory Models, Statistical Methods, and Applications Third Edition Marvin Rausand Norwegian University of Science & Technology Trondheim, Norway Anne Barros CentraleSupélec, Paris-Saclay University Paris, France Arnljot Høyland† Norwegian University of Science & Technology Trondheim, Norway

4 Copyright

5 dedication-page

6 Preface Main Changes from the Second Edition Supplementary Information on the Internet Intended Audience Aims and Delimitation Authors Acknowledgments References

7 About the Companion Website Open Site Instructor Site GitHub Site Contact Person

8 1 Introduction1.1 What is Reliability? 1.2 The Importance of Reliability 1.3 Basic Reliability Concepts 1.4 Reliability Metrics 1.5 Approaches to Reliability Analysis 1.6 Reliability Engineering 1.7 Objectives, Scope, and Delimitations of the Book 1.8 Trends and Challenges 1.9 Standards and Guidelines 1.10 History of System Reliability 1.11 Problems References

9 2 The Study Object and its Functions2.1 Introduction 2.2 System and System Elements 2.3 Boundary Conditions 2.4 Operating Context 2.5 Functions and Performance Requirements 2.6 System Analysis 2.7 Simple, Complicated, and Complex Systems 2.8 System Structure Modeling 2.9 Problems References

10 Chapter 3: Failures and Faults3.1 Introduction 3.2 Failures 3.3 Faults 3.4 Failure Modes 3.5 Failure Causes and Effects 3.6 Classification of Failures and Failure Modes 3.8 Problems References

11 Chapter 4: Qualitative System Reliability Analysis4.1 Introduction 4.2 FMEA/FMECA 4.3 Fault Tree Analysis 4.4 Event Tree Analysis 4.5 Fault Trees versus Reliability Block Diagrams 4.6 Structure Function 4.7 System Structure Analysis 4.8 Bayesian Networks 4.9 Problems References

12 5 Probability Distributions in Reliability Analysis 5.1 Introduction 5.2 A Dataset 5.3 General Characteristics of Time‐to‐Failure Distributions 5.4 Some Time‐to‐Failure Distributions 5.5 Extreme Value Distributions 5.6 Time‐to‐Failure Models With Covariates 5.7 Additional Continuous Distributions 5.8 Discrete Distributions 5.9 Classes of Time‐to‐Failure Distributions 5.10 Summary of Time‐to‐Failure Distributions 5.11 Problems References

13 6 System Reliability Analysis 6.1 Introduction 6.2 System Reliability 6.3 Nonrepairable Systems 6.4 Standby Redundancy 6.5 Single Repairable Items 6.6 Availability of Repairable Systems 6.7 Quantitative Fault Tree Analysis 6.8 Event Tree Analysis 6.9 Bayesian Networks 6.10 Monte Carlo Simulation 6.11 Problems References

14 7 Reliability Importance Metrics7.1 Introduction 7.2 Critical Components 7.3 Birnbaum's Metric for Structural Importance 7.4 Birnbaum's Metric of Reliability Importance 7.5 Improvement Potential 7.6 Criticality Importance 7.7 Fussell–Vesely's Metric 7.8 Differential Importance Metric 7.9 Importance Metrics for Safety Features 7.10 Barlow–Proschan's Metric 7.11 Problems References

15 8 Dependent Failures8.1 Introduction 8.2 Types of Dependence 8.3 Cascading Failures 8.4 Common‐Cause Failures 8.5 CCF Models and Analysis 8.6 Basic Parameter Model 8.7 Beta‐Factor Model 8.8 Multi‐parameter Models 8.9 Problems References

16 9 Maintenance and Maintenance Strategies9.1 Introduction 9.2 Maintainability 9.3 Maintenance Categories 9.4 Maintenance Downtime 9.5 Reliability Centered Maintenance 9.6 Total Productive Maintenance 9.7 Problems References

17 10 Counting Processes10.1 Introduction 10.2 Homogeneous Poisson Processes 10.3 Renewal Processes 10.4 Nonhomogeneous Poisson Processes 10.5 Imperfect Repair Processes 10.6 Model Selection 10.7 Problems References

18 11 Markov Analysis11.1 Introduction 11.2 Markov Processes 11.3 Asymptotic Solution 11.4 Parallel and Series Structures 11.5 Mean Time to First System Failure 11.6 Systems with Dependent Components 11.7 Standby Systems 11.8 Markov Analysis in Fault Tree Analysis 11.9 Time‐Dependent Solution 11.10 Semi‐Markov Processes 11.11 Multiphase Markov Processes 11.12 Piecewise Deterministic Markov Processes 11.13 Simulation of a Markov Process 11.14 Problems References

19 12 Preventive Maintenance12.1 Introduction 12.2 Terminology and Cost Function 12.3 Time‐Based Preventive Maintenance 12.4 Degradation Models 12.5 Condition‐Based Maintenance 12.6 Maintenance of Multi‐Item Systems 12.7 Problems References

20 Chapter 13: Reliability of Safety Systems13.1 Introduction 13.2 Safety‐Instrumented Systems 13.3 Probability of Failure on Demand 13.4 Safety Unavailability 13.5 Common Cause Failures 13.6 CCFs Between Groups and Subsystems 13.7 IEC 61508 13.8 The PDS Method 13.9 Markov Approach 13.10 Problems References

21 14 Reliability Data Analysis14.1 Introduction 14.2 Some Basic Concepts 14.3 Exploratory Data Analysis 14.4 Parameter Estimation 14.5 The Kaplan–Meier Estimate 14.6 Cumulative Failure Rate Plots 14.7 Total‐Time‐on‐Test Plotting 14.8 Survival Analysis with Covariates 14.9 Problems References

22 15 Bayesian Reliability Analysis15.1 Introduction 15.2 Bayesian Data Analysis 15.3 Selection of Prior Distribution 15.4 Bayesian Estimation 15.5 Predictive Distribution 15.6 Models with Multiple Parameters 15.7 Bayesian Analysis with R 15.8 Problems References

23 16 Reliability Data: Sources and Quality16.1 Introduction 16.2 Generic Reliability Databases 16.3 Reliability Prediction 16.4 Common Cause Failure Data 16.5 Data Analysis and Data Quality 16.6 Data Dossier References

24 Appendix A: Appendix AAcronyms

25 Appendix B: Appendix BLaplace Transforms B.1 Important Properties of Laplace Transforms B.2 Laplace Transforms of Some Selected Functions

26 Author Index

27 Subject Index

28 Wiley Series in Probability and Statistics

29 End User License Agreement

1 Chapter 1 Table 1.1 Availability and downtime.

2 Chapter 4 Table 4.1 Deductive versus inductive methods. Table 4.2 Occurrence rating (example). Table 4.3 Severity rating (example). Table 4.4 Fault tree symbols. Table 4.5 Criticality ranking of minimal cut sets of order 2. Table 4.6 Truth table for a 2oo3 structure.Table 4.7 Truth table for a series structure of two components.Table 4.8 Truth table for a parallel structure of two components.Table 4.9 Truth table for the 2oo3 structure.

3 Chapter 5Table 5.1 Historical dataset.Table 5.2 Relationship between the functions , and .Table 5.3 Summary of time‐to‐failure distributions and parameters.

4 Chapter 6Table 6.1 A brief comparison of the structures (1), (2), and (3).Table 6.2 MTTF of some oo structures of identical and independent components...Table 6.3 Prior probability of root node .Table 6.4 Conditional probability table for two nodes.Table 6.5 Prior probability of the root nodes and .Table 6.6 Table for Problem 6.10.