System Reliability Theory. Marvin Rausand

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 Analysis 14.1 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 Analysis 15.1 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 Quality 16.1 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

      List of Tables

      1 Chapter 1Table 1.1 Availability and downtime.

      2 Chapter 4Table 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.

      5 Chapter 7Table 7.1 Critical path vectors for component 1.

      6 Chapter 10Table 10.1 Failure times (operating days) in chronological order.Table 10.2 Data set for Problem 13.

      7 Chapter 11Table 11.1 Possible states of a structure of two components.Table 11.2 Possible states of a series structure of two components where fail...Table 11.3 The possible states of a two‐item parallel system with cold standb...

      8 Chapter 13Table 13.1 PFD of some oo structures of identical and independent components...Table 13.2 PFD and spurious trip rate for three simple structures.Table 13.3 Safety integrity levels for safety functions.Table 13.4 Failure rates for the “fail to function” mode.

      9 Chapter