##
**Bayesian reliability analysis.**
*(English)*
Zbl 0597.62101

Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. Chichester etc.: John Wiley &\(\vdots Sons\) Ltd. XX, 745 p. (1982).

The authors state in the preface that ”The primary purpose of this book is to aggregate and systematically introduce both the numerous and varied Bayesian techniques for analysis of reliability data. Our intent is to introduce the basic notions that constitute a Bayesian reliability analysis, present the many analytic methods, illustrate the application of Bayesian procedures, and catalog the relevant Bayesian reliability literature.” In the reviewer’s opinion, the authors have succeeded to a large extent.

This book is the first one of its kind devoted exclusively to Bayesian methods for reliability analysis. This comprehensive reference/text amply justifies the authors’ claim that, ”although there exist numerous books that present the basic ideas of classical reliability analyses”, this book focuses attention on Bayesian techniques. ”Today’s emphasis on increased productivity in high technology industries has heightened interest in developing reliability analysis techniques which utilize all available information - both objective test data and subjective information - in a cost-effective way.” In recent years, one has witnessed the growth and implementation of several Bayesian reliability analysis methods, which meet these necessities.

This book gives a thorough account of the most frequently used statistical techniques of Bayesian reliability analysis and systematically introduces the major contributions in this field during the past two decades. Most of the text is addressed to reliability engineers, quality assurance specialists, and systems and risk analysts, and gives them a single-source guide to these powerful techniques. Many of the numerical examples presented in the book are derived from real research situations. These have a real data component and are based on reliability data developed for the U.S. commercial nuclear reactor industry. These examples illustrate the methods presented in the text, which make it valuable to managers and engineers as well as to those who are engaged in planning or performing experiments in reliability studies.

Chapter 1 is introductory and serves the purpose of a general layout for the text. Chapters 2, 3 and 4 present necessary background material for the sake of completeness. The fundamental ideas and relevant distributions for use in classical reliability analyses are discussed in Chapter 4. Chapter 5 is used to introduce the basic notions of Bayesian inference for reliability theory. The problem of selecting prior distributions in Bayesian analyses is discussed in Chapter 6. Chapter 7 addresses the problem of using the attribute life test data in estimating relevant quantities in equipment performance studies. Chapters 8 and 9 are concerned with analyses using the standard continuous lifetime probability distributions.

The second half of the book is concerned with more specialized topics, such as reliability demonstration testing, system reliability assessment, availability of maintained systems, and empirical Bayes reliability estimation. These topics are presented from a Bayesian perspective. The assessment of the reliability of a system is often required in industrial, military and everyday situations. For such an assessment, it is important to specify the configuration of components, the failure mode of each component and the states in which the system is using component data for series, parallel and r-out-of-k systems. In Chapter 11, Bayesian estimation is considered only for nonmaintained systems.

Chapter 12 considers system availability - a measure of the effectiveness of a maintained system that incorporates the concepts of reliability and maintainability. The last chapter departs markedly in philosophy from the rest of the book. It addresses a fundamental question: Can the Bayesian procedure be used if the underlying prior distribution is unidentified? The theoretical structure of the methodology known as empirical Bayes decision procedure is presented in this chapter.

The authors point out, and the reviewer agrees with their opinion, that this book can serve as an excellent text for advanced undergraduate and graduate courses on Bayesian reliability analysis. Throughout the book, the authors give equal emphasis to estimation and hypothesis testing and discuss which of these techniques is appropriate in a particular situation. The book discusses many excellent examples and problems from different fields of application. Thus, the book is appropriate for a ”general” introductory course on Bayesian methods on reliability analysis. One unique feature of the book is the use of reliability data developed for the U.S. commercial nuclear reactor industry.

Overall, the book is readable, carefully written, well motivated, and utilizes many interesting examples. It certainly deserves serious consideration for use in a general introductory Bayesian statistics course. It would serve well, especially the reliability engineers and systems analysts. It is well suited for its intended audience as a solid introduction to Bayesian reliability theory and analysis and offers the reader something extra. The practical examples show the reader the many areas in which the Bayesian theory can be applied and the importance of correctly interpreting results in reliability data analysis.

In summary, the book is the result of an outstanding effort by the authors in bringing to light the powerful and newly-emerged subject of Bayesian reliability methods.

This book is the first one of its kind devoted exclusively to Bayesian methods for reliability analysis. This comprehensive reference/text amply justifies the authors’ claim that, ”although there exist numerous books that present the basic ideas of classical reliability analyses”, this book focuses attention on Bayesian techniques. ”Today’s emphasis on increased productivity in high technology industries has heightened interest in developing reliability analysis techniques which utilize all available information - both objective test data and subjective information - in a cost-effective way.” In recent years, one has witnessed the growth and implementation of several Bayesian reliability analysis methods, which meet these necessities.

This book gives a thorough account of the most frequently used statistical techniques of Bayesian reliability analysis and systematically introduces the major contributions in this field during the past two decades. Most of the text is addressed to reliability engineers, quality assurance specialists, and systems and risk analysts, and gives them a single-source guide to these powerful techniques. Many of the numerical examples presented in the book are derived from real research situations. These have a real data component and are based on reliability data developed for the U.S. commercial nuclear reactor industry. These examples illustrate the methods presented in the text, which make it valuable to managers and engineers as well as to those who are engaged in planning or performing experiments in reliability studies.

Chapter 1 is introductory and serves the purpose of a general layout for the text. Chapters 2, 3 and 4 present necessary background material for the sake of completeness. The fundamental ideas and relevant distributions for use in classical reliability analyses are discussed in Chapter 4. Chapter 5 is used to introduce the basic notions of Bayesian inference for reliability theory. The problem of selecting prior distributions in Bayesian analyses is discussed in Chapter 6. Chapter 7 addresses the problem of using the attribute life test data in estimating relevant quantities in equipment performance studies. Chapters 8 and 9 are concerned with analyses using the standard continuous lifetime probability distributions.

The second half of the book is concerned with more specialized topics, such as reliability demonstration testing, system reliability assessment, availability of maintained systems, and empirical Bayes reliability estimation. These topics are presented from a Bayesian perspective. The assessment of the reliability of a system is often required in industrial, military and everyday situations. For such an assessment, it is important to specify the configuration of components, the failure mode of each component and the states in which the system is using component data for series, parallel and r-out-of-k systems. In Chapter 11, Bayesian estimation is considered only for nonmaintained systems.

Chapter 12 considers system availability - a measure of the effectiveness of a maintained system that incorporates the concepts of reliability and maintainability. The last chapter departs markedly in philosophy from the rest of the book. It addresses a fundamental question: Can the Bayesian procedure be used if the underlying prior distribution is unidentified? The theoretical structure of the methodology known as empirical Bayes decision procedure is presented in this chapter.

The authors point out, and the reviewer agrees with their opinion, that this book can serve as an excellent text for advanced undergraduate and graduate courses on Bayesian reliability analysis. Throughout the book, the authors give equal emphasis to estimation and hypothesis testing and discuss which of these techniques is appropriate in a particular situation. The book discusses many excellent examples and problems from different fields of application. Thus, the book is appropriate for a ”general” introductory course on Bayesian methods on reliability analysis. One unique feature of the book is the use of reliability data developed for the U.S. commercial nuclear reactor industry.

Overall, the book is readable, carefully written, well motivated, and utilizes many interesting examples. It certainly deserves serious consideration for use in a general introductory Bayesian statistics course. It would serve well, especially the reliability engineers and systems analysts. It is well suited for its intended audience as a solid introduction to Bayesian reliability theory and analysis and offers the reader something extra. The practical examples show the reader the many areas in which the Bayesian theory can be applied and the importance of correctly interpreting results in reliability data analysis.

In summary, the book is the result of an outstanding effort by the authors in bringing to light the powerful and newly-emerged subject of Bayesian reliability methods.

### MSC:

62N05 | Reliability and life testing |

62F15 | Bayesian inference |

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |

62C10 | Bayesian problems; characterization of Bayes procedures |

90B25 | Reliability, availability, maintenance, inspection in operations research |