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 for engineers concerned with the design of physical systems such as civil structures, power plants, and transport vehicles of all types. Increasing public concern with the reliability o~ systems for reasons of human safety, environmental protection, and acceptable ir. vestment risk limitations has resulted in an increasing interest by engineers in the formal applica~i0n of reliability theory to e~gineering desian. At the same time there is a demand for more effective approaches to the des~gn of procedures for the operation and use of man-made syste~s and more meaningful assessment of the risks intr)duction and use of 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.

Preface.- 1.0 Introduction.- 2.0 Fundamental Concepts.- 2.A Basic Concepts of Probability and Statistics.- 3.0 Assessment of Reliability Function.- 4.0 Reliability of Series and Parallel Systems.- Appendix 4.A A Systems Example.- 5.0 Failure Mode and Effects Analysis — Fault Tree Analyses.- 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.- Appendix 5.A Performance of a Failure Mode and Effects Analysis.- Appendix 5.B Performance of a Maintainability Engineering Analysis.- 6.0 Multivariate Probability Distribution and Stochastic Processes.- 6.1 Multivariate Probability Distributions.- 6.2 Stochastic Processes.- 6.3 Markov Processes.- Appendix 6.A Introduction to Matrix Algebra.- Appendix 6.B Z-Transform Methods for Markov Chains.- Appendix 6.C Laplace Transformation.- 7.0 Testing for Markov Properties.- 7.1 Estimation of Transition Probabilities.- 7.2 Chi-Square Approximation to Multinominal Density.- 7.3 Testing Hypothesis Using Chi-Square Density.- 7.4 Test to Determine if the Observed nij’s Are From a Markov Chain with Transition Probabilities Pij.- 7.5 Test to Determine Stationarity of Transition Probabilities.- 7.6 Test to Determine Independence of Observed Transition Frequencies nij.- 7.7 Test to Determine if Process is First or Second Order Markov Chain.- 7.8 Test to Determine if Markov Chains Are Identical.- 7.9 Example of Chi-Square Tests.- 7.10 The Likelihood Ratio Tests.- 7.11 Continuous Time Parameter Markov Processes.- 8.0 The Generalized Failure Process for Nonmaintained Systems.- 8.1 Solution Using Laplace Transforms.- 8.2 Stand-By (Off Line) Redundant System.- 8.3 Series System.- 8.4 Redundant (On Line) Parallel System.- 8.5 State Dependent Reliability Models.- 8.6 Linear Stress Models.- 8.7 The Effect of Switching.- 9.0 Analyses of Maintained System.- 9.1 Systems Availability.- 9.2 Markov Models for Maintained Systems.- 9.2.1 Maintained Series Systems.- 9.2.2 Maintained Parallel Systems.- 9.3 Development of the General Expression for the Mean Time to Failure of a Markov Chain.- 9.3.1 Mean Time to Failure and Variance of Time to Failure of Non-Maintained and Maintained Systems.- 9.4 Models of Maintained Systems With Redundant Off-Line Components.- Appendix 9.A Analysis of Non-Markovian Systems.- Appendix 9.B Introduction to Flowgraphs.- Appendix 9.C Introduction to GERT.- 10.0 Strategies for Repair Policies.- 10.0.1 General Repair Strategy Determination.- 10.0.2 Cost of Scheduled Overhauls and Inspections.- 10.0.3 Spare Part Inventory Provisioning.- 10.1 Use of Dynamic Programming in Systems Reliability.- 10.1.1 Complex System Reliability — Analysis Under Constraints.- 10.2 The Use of the Lagrange Multiplier Method.- 10.2.1 Systems Involving Two Types of Constraints.- 10.3 Optimum Maintenance Policies by Dynamic Programming.- 10.4 Spare Part Provisioning Models.- 10.5 Systems Performance Evaluation.- 11.0 Effects Of Component Interaction.- 11.1 Effect of Interaction of Component Reliability.- 11.2 Analysis of Wear Rates.- 11.3 Component Reliability.- 11.4 System Reliability.- 11.5 Use of Networks in the Analysis of Interactive Systems Reliability, Maintainability, and Availability.- 12.0 Application Of Fault Tree And Other Network Techniques.- 12.1 Implementation of Fault Tree Analysis.- 12.1.1 Representing Fault Trees by Networks.- 12.1.2 Uncertainty in Reliability Analysis.- 13.0 Reliability And Risk In Perspective.- 13.1 Analysis of Risk.- 13.1.1 Reliability and Risk Assessment.- 13.2 Issues and Concerns.- Tables.- Standard Normal Curve.- Table of Exponential Functions.- Required Number of Failures.- t-Function.- Gamma Function.