Mathematical theory of reliability

Richard E. Barlow, Frank Proschan9780898713695, 0898713692

This monograph presents a survey of mathematical models useful in solving reliability problems. It includes a detailed discussion of life distributions corresponding to wearout and their use in determining maintenance policies, and covers important topics such as the theory of increasing (decreasing) failure rate distributions, optimum maintenance policies, and the theory of coherent systems. The emphasis throughout the book is on making minimal assumptions – and only those based on plausible physical considerations – so that the resulting mathematical deductions may be safely made about a large variety of commonly occurring reliability situations. The first part of the book is concerned with component reliability, while the second part covers system reliability, including problems that are as important today as they were in the 1960s. The enduring relevance of the subject of reliability and the continuing demand for a graduate-level book on this topic are the driving forces behind its re-publication.

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Table of contents :
Mathematical Theory of Reliability……Page 1
Contents……Page 8
Preface to the Classics Edition……Page 12
Preface……Page 14
Acknowledgments……Page 18
CHAPTER 1 Introduction……Page 20
CHAPTER 2 Failure Distributions……Page 28
CHAPTER 3 Operating Characteristics of Maintenance Policies……Page 65
CHAPTER 4 Optimum Maintenance Policies……Page 103
CHAPTER 5 Stochastic Models for Complex Systems……Page 138
CHAPTER 6 Redundancy Optimization……Page 181
CHAPTER 7 Qualitative Relationships for Multicomponent Structures……Page 217
APPENDIX 1 Total Positivity……Page 248
APPENDIX 2 Test for Increasing Failure Rate……Page 253
APPENDIX 3 Tables Giving Bounds on Distributions with Monotone Failure Rate……Page 257
References……Page 262
Author Index……Page 270
Subject Index……Page 272