##
**System reliability theory. Models and statistical methods.**
*(English)*
Zbl 0846.93001

New York, NY: John Wiley & Sons Ltd. x, 518 p. (1994).

This book intends to present a comprehensive introduction to component and system reliability theory. It consists of 12 chapters, 6 appendices, more than 200 references, an author index and a subject index.

First, five chapters are devoted to systems where the state variables are binary and independent, and they cover fundamental areas of system reliability theory. The remaining chapters are more advanced and topical.

Chapter 1 presents a brief history of reliability technology, basic concepts in reliability and its application areas. In Chapter 2, several quantitative measures for the reliability of an unrepaired unit (e.g. reliability function \(R(t)\), failure rate \(z(t)\) and mean time to failure (MTBF)) and important probability distributions in reliability theory (e.g. exponential, gamma, Pareto, Weibull, normal, lognormal, Birnbaum-Saunders, inverse Gaussian, extreme value distributions) are introduced. Chapter 3 considers the structural relationship between a system and its components and shows how a deterministic model of the structure can be established by using a reliability block diagram or a fault tree. Chapter 4 discusses the general characteristic of system reliability for systems with \(n\) components where failures of the individual components can be interpreted as independent events. The discussion indicates that the reliability importance of a component in a system depends on its location in the system and several measures of the reliability importance (e.g. Birnbaum, criticality importance, Vesely-Fussel and improvement potential measures) are given in Chapter 5. Chapter 6 introduces the state-space method of system reliability for the analysis of the components and systems which have a finite set of states. Here, the system states and the possible transitions are described by a state-space diagram (Markov diagram). The concepts of counting processes such as homogeneous Poisson processes (HPP), renewal processes and nonhomogeneous Poisson processes (NHPP) are introduced in Chapter 7 for the analysis of a repairable system. Chapter 8 discusses briefly the dependent failure cases. In Chapter 9, a broad introduction to life data analysis to obtain information about a particular life distribution \(F(t)\) for complete and censored data sets is given. Chapter 10 presents a brief discussion for accelerated life testing. Chapter 11 illustrates how the Bayesian approach is used in the reliability analysis. Brief comments on data books and data banks in Chapter 12 conclude this book. The appendices define the gamma and beta distributions, provide distribution theorems, describe maximum likelihood estimation, Laplace transforms, basic terms and concepts in reliability and statistical tables. The problems at the end of each chapters provide exercises and further applications.

Though some chapters of the second half of this book are described too briefly, this book is as a whole well organized and written clearly. It can be recommended as a text for undergraduate (Chapters 1-5) and graduate students (Chapters 6-11) and also as a reference book for reliability engineers.

First, five chapters are devoted to systems where the state variables are binary and independent, and they cover fundamental areas of system reliability theory. The remaining chapters are more advanced and topical.

Chapter 1 presents a brief history of reliability technology, basic concepts in reliability and its application areas. In Chapter 2, several quantitative measures for the reliability of an unrepaired unit (e.g. reliability function \(R(t)\), failure rate \(z(t)\) and mean time to failure (MTBF)) and important probability distributions in reliability theory (e.g. exponential, gamma, Pareto, Weibull, normal, lognormal, Birnbaum-Saunders, inverse Gaussian, extreme value distributions) are introduced. Chapter 3 considers the structural relationship between a system and its components and shows how a deterministic model of the structure can be established by using a reliability block diagram or a fault tree. Chapter 4 discusses the general characteristic of system reliability for systems with \(n\) components where failures of the individual components can be interpreted as independent events. The discussion indicates that the reliability importance of a component in a system depends on its location in the system and several measures of the reliability importance (e.g. Birnbaum, criticality importance, Vesely-Fussel and improvement potential measures) are given in Chapter 5. Chapter 6 introduces the state-space method of system reliability for the analysis of the components and systems which have a finite set of states. Here, the system states and the possible transitions are described by a state-space diagram (Markov diagram). The concepts of counting processes such as homogeneous Poisson processes (HPP), renewal processes and nonhomogeneous Poisson processes (NHPP) are introduced in Chapter 7 for the analysis of a repairable system. Chapter 8 discusses briefly the dependent failure cases. In Chapter 9, a broad introduction to life data analysis to obtain information about a particular life distribution \(F(t)\) for complete and censored data sets is given. Chapter 10 presents a brief discussion for accelerated life testing. Chapter 11 illustrates how the Bayesian approach is used in the reliability analysis. Brief comments on data books and data banks in Chapter 12 conclude this book. The appendices define the gamma and beta distributions, provide distribution theorems, describe maximum likelihood estimation, Laplace transforms, basic terms and concepts in reliability and statistical tables. The problems at the end of each chapters provide exercises and further applications.

Though some chapters of the second half of this book are described too briefly, this book is as a whole well organized and written clearly. It can be recommended as a text for undergraduate (Chapters 1-5) and graduate students (Chapters 6-11) and also as a reference book for reliability engineers.

Reviewer: K.Uosaki (Tottori)

### MSC:

93-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory |

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

62N05 | Reliability and life testing |

60K10 | Applications of renewal theory (reliability, demand theory, etc.) |