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Detailed review of: 

Stochastic Ageing and Dependence for Reliability





Springer Verlag




Chin-Diew Lai and Min Xie




Stochastic Ageing and Dependence for Reliability


Year of Publication














Suprasad V. Amari




Review published in IJPE, Vol. 3, No. 2, April 2007, p. 292.

Table of Contents
  1. Introduction (6 pages)
  2. Concepts and Applications of Stochastic Ageing (64 pages)
  3. Bathtub Shaped Failure Rate Life Distributions (37 pages)
  4. Mean Residual Life – Concepts and Applications in Reliability Analysis (30 pages)
  5. Weibull Related Distributions (28 pages)
  6. An Introduction to Discrete Failure Time Models (36 pages)
  7. Tests of Stochastic Ageing (34 pages)
  8. Bivariate and Multivariate Ageing (22 pages)
  9. Concepts and Measures of Dependence in Reliability (48 pages)
  10. Reliability of Systems with Dependent Components (38 pages)
  11. Failure Time Data (18 pages)
  • References  (44 pages)
  • Index  (10 pages)

This book is an important addition to several well-written books on reliability theory and concepts.

The book fulfills the authors aim in providing a comprehensive treatment of both ageing and dependence concepts, with emphasis on reliability and survival analysis. The book has a forward by Dr. Richard E. Barlow, a pioneer in the field of reliability theory. As mentioned by Barlow, the book covers most of the results in the literature pertaining to ageing classes and bivariate life distributions; as a result, it can be regarded as a compendium of ageing concepts. The book is encyclopedic in scope and will be useful to both practitioners and researchers in reliability engineering as well as other disciplines. The book is written at a relatively advanced level, which means that readers should have some basic knowledge in probability and statistics before reading it. 

Important features of this book are that it contains a comprehensive list of references (44 pages and nearly 800 entries) and provides up-to-date information on what has been written on the subject to date. Many important results of the last three decades are brought together and succinctly summarized. Readers interested in the details, however, can easily refer to the corresponding cited references for detailed proofs.

The book begins with discussion of various concepts of stochastic ageing, starting with the definition of the failure rate function (or hazard function). The remarks on terminology explain the reasons for the continued usage of the term "failure rate" instead of "hazard rate." The book presents detailed descriptions of life distributions belonging to various classes of failure rate functions and mean residual life distributions. Various families of "bathtub-shaped" failure rate distributions are presented in detail. A complete chapter is devoted to the Weibull distribution and its generalizations, which can be flexible in modeling various sources of lifetime data. Discrete failure time distributions and their ageing concepts are also discussed in detail. The book includes a wide range of statistical tests on ageing that helps in determining which ageing class data belongs to, which is an important starting point in analyzing any failure data. The discussion on reliability of systems with dependent components is very important for accurate reliability analysis as component lifetimes are generally dependent in practice. The book also presents 33 data sets of failure times that could be useful for researchers and students in their future study in this field.

Overall, I recommend this book to all serious-minded researchers, practitioners, teachers, and graduate students who would like to have the most up-to-date information available on the subject of stochastic ageing and dependencies in reliability. It also serves as reference book on reliability and survival analysis and is a good addition to one's statistical or reliability library.

Suprasad V. Amari


Review published in the International Journal of Performability Engineering, Vol. 3, No. 2, April 2007, p. 292. 


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