Systems Reliability and Risk Analysis

Ernst G. Frankel This book has its origin in lecture notes developed over several years for use in a course in Systems Reliability f~r engineers concerned with the design of physical systems such as civil structures, power plants, and transport systems of all types. Increasing public concern with the reliability of systems for reasons of human safety, environmental protection, and acceptable investment risk limitations has resulted in an increasing interest by engineers in the formal application of reliability theory to engineering design. At the same time there is a demand for more effective approaches to the design of procedures for the operation and use of man­ made systems, more meaningful assessment of the risks introduced, and use such a system poses both when operating as designed and when operating at below design performance. The purpose of the book is to provide a sound, yet practical, introduction to reliability analysis and risk assessment which can be used by professionals in engineering, planning, management, and economics to improve the design, operation, and risk assessment of systems of interest. The text should be useful for students in many disciplines and is designed for fourth-year undergraduates or first-year graduate students. I would like to acknowledge the help of many of my graduate students who contributed to the development of this book by offering comments and criticism. Similarly, I would like to thank Mrs. Sheila McNary who typed untold drafts of the manuscript, and Mr.

1.0 Introduction.- 1.1 Suggested Readings.- 2.0 Fundamental Concepts.- 2.1 Basic Concepts of Reliability.- 2.2 References.- 3.0 Assessment of Reliability Function.- 3.1 Non-parametric Reliability Function Assessment.- 3.2 Parametric Reliability Function Assessment.- 3.3 Exercises.- 3.4 References.- 4.0 Reliability of Series and Parallel Systems.- 4.1 Simple Series Systems.- 4.1.1 Application to Components with Exponential Failure Densities.- 4.2 Simple Parallel Systems.- 4.2.1 Relation Between MTBF and R(t) in Simple Exponential Redundant System.- 4.3 Variations of Simple Redundant Systems.- 4.4 Analysis of Complex Series Redundant System.- 4.5 Off-Line Redundant Systems.- 4.6 Exercises.- 4.7 References.- 5.0 Failure Mode and Effects Analysis — Fault Tree Analysis.- 5.1 Common Cause Failure.- 5.2 Complex System Reliability Networks.- 5.3 Fault Tree Analysis.- 5.3.1 Min Cut Sets of Fault Trees.- 5.4 Exercises.- 5.5 References.- Appendix 5A Performance of a Failure Mode and Effects Analysis.- Appendix 5B Performance of a Maintainability Engineering Analysis (MEA).- 6.0 Multivariable Probability Distributions and Stochastic Processes.- 6.1 Multivariable Probability Distributions.- 6.2 Stochastic Processes.- 6.3 Markov Processes.- 6.4 Exercises.- 6.5 References.- 7.0 The Generalized Failure Process for Non-Maintained Systems.- 7.1 Solution Using Laplace Transforms.- 7.2 Stand-by (Off Line) Redundant System.- 7.3 Series Systems.- 7.4 Redundant (On-Line) Parallel Systems.- 7.5 State-Dependent Reliability Models.- 7.6 Linear Stress Model.- 7.7 The Effect of Switching.- 7.8 Exercises.- 7.9 References.- 8.0 Analysis of Maintained Systems.- 8.1 Systems Availability.- 8.2 Markov Models for Maintained Systems.- 8.2 Maintained Series Systems.- 8.2 Maintained Parallel Systems.- 8.3 Development of the General Expression for the Mean Time to Failure of a Markov Chain.- 8.3.1 Mean Time to Failure and Variance of Time to Failure of Non-Maintained and Maintained Systems.- 8.4 Models of Maintained Systems with Redundant Off-Line Components.- 8.5 Exercises.- 8.6 References.- 9.0 Strategies for Repair Policies.- 9.0.1 General Repair Strategy Determination.- 9.0.2 Cost of Scheduled Overhauls and Inspections.- 9.0.3 Spare Pare Inventory Provisioning.- 9.1 Use of Dynamic Programming in Systems Reliability.- 9.1.1 Complex system Reliability Analysis Under Constraints.- 9.1.2 Optimization of Multistage Decision Processes.- 9.1.3 Complex System with Component Stand-by.- 9.1.4 Complex System with Switching.- 9.1.5 Reliability of Complex System with Component Maintenance.- 9.1.6 Analysis of Component Failure.- 9.1.7 Conclusions.- 9.2 The Use of the Lagrange Multiplier Method.- 9.2.1 System Involving Two Types of Constraints.- 9.3 Optimum Maintenance Policies by Dynamic Programming.- 9.4 Spare Part Provisioning Models.- 9.5 System Performance Evaluation.- 9.6 Exercises.- 9.7 References.- 10.0 Effects of Component Interaction.- 10.1 Effect of Interaction of Component Reliability.- 10.2 Analysis of “Wear” Rates.- 10.3 Component Reliability.- 10.4 System Reliability.- 10.5 Use of Networks in the analysis of Interactive Systems Reliability, Maintainability, and Availability.- 10.6 Exercises.- 10.7 References.- 11.0 Application of Fault Tree and Other Network Techniques.- 11.1 Implementation of Fault Tree Analysis.- 11.1.1 Representing Fault Trees by Networks.- 11.2 Uncertainty in Reliability Analysis.- 11.2.1 GERT Reliability Networks with Uncertainty.- 11.3 References.- 12.0 Reliability and Risk in Perspective.- 12.1 General Considerations.- 12.1 Risk Attitudes.- 12.2 Analysis of Risk.- 12.2.1 Reliability and Risk Assessment.- 12.3 Issues and Concerns.- Appendix A Basic Concepts of Probability and Statistics.- Appendix B Matrix Algebra and Transformations.- Appendix C Testing for Markov Properties.- Appendix D Non-Markovian Systems.- Appendix E Introduction to Flow Graphs and Gert.- Appendix F Statistical Tables.