The book is a welcome addition to the ever growing list of texts and monographs in the area of reliability theory and survival analysis. The first two chapters introduce the reader to the basic ideas of reliability theory. The notions of structure function, path sets, cut sets and modules are introduced, studied and illustrated. Several methods for obtaining bounds on the system reliability are discussed. Of a particular interest is the description of an approximation to the system reliability when the components are highly reliable. The exponential, Weibull, gamma, normal and some related distributions with nonnegative supports are defined and their properties are studied. The aging notions of IFR, IFRA, NBU, NBUE and their relatives are described and compared. Also given are some bounds on the reliability of various systems under the assumption that the components age with time.
Chapter 3 discusses reliability systems with renewable components, that is, components which are sent to a repair facility upon failure and have random repair durations. The emphasis in this chapter is on systems with components for which the repair duration is short in relation to their lifetimes. Such situations are called “fast repair”. The approximation of the time to first failure distribution of such systems to the exponential distribution is highlighted. Both exponential and arbitrary distributed repair times are considered.
Optimal preventive maintenance policies and the optimal use of redundant standby components are discussed in Chapter 4. It is shown how to obtain the optimum in several models of interest which have not been discussed yet in any other text or monograph in reliability theory. Also the classical models of age replacement and block replacement policies are described in this chapter. The optimum is found for both the finite and the infinite time horizon.
Chapter 5, which by itself consists of about half of the monograph, discusses some statistical aspects of reliability theory. Various methods of nonparametric estimation of the reliability function are described. This is done for sets of data of different forms such as complete observations, censored observations, partly censored observations and so on. Some lifetime models with concomitant variables are also described in this chapter. The basic ideas of accelerated life testing are touched upon. Confidence intervals and procedures for hypotheses testing for such models are described and illustrated. Also some statistical inference for parametric models, such as the exponential and the Weibull distributions, is considered. The proportional hazard model of Cox is also studied. Finally, confidence intervals procedures for the system availability and reliability are discussed.
The first two chapters of the monograph overlap with some of the material in the book, “Statistical theory of reliability and life testing”. (1975; Zbl 0379.62080), by R. E. Barlow and F. Proschan. But this overlap is welcome since the examples are different and novel, and the author tries to highlight the intuition beyond the definitions and the numerical examples. In fact every procedure which is described in this text is illustrated numerically so that the reader can appreciate the numerical difficulties, if any, of the theoretical results.
The author tries hard and succeeds in giving the intuitive meaning of many of the mathematical definitions and results which are given in the text. Each chapter has a multitude of exercises, all of which have detailed solutions at the end of the book. Also, each chapter has a section of comments and notes which includes references for further study. Overall, this is a text that any worker in reliability theory may consider having on his or her bookshelf. As the author claims, this book may also be used as text for an advanced graduate course in reliability theory.
Reviewer: M.Shaked
[-]The book is a welcome addition to the ever growing list of texts and monographs in the area of reliability theory and survival analysis. The first two chapters introduce the reader to the basic ideas of reliability theory. The notions of structure function, path sets, cut sets and modules are introduced, studied and illustrated. Several methods for obtaining bounds on the system reliability are discussed. Of a particular interest is the ...
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