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Mathematical theory of reliability. With contributions by Larry C. Hunter. (English) Zbl 0874.62111
Classics in Applied Mathematics. 17. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. xv, 258 p. (1996).
This “Mathematical Theory of Reliability” by Richard E. Barlow and Frank Proschan is one of the best books on reliability. It addresses the needs of applied mathematicians and at the same time provides a rigorous presentation of the required probability background. Generations of applied mathematicians from all over the world were introduced to reliability by this book. They were captured forever into the mysterious world of applied mathematics by the ideas and the beauty of the presentation.
The book consists of two parts: The first one is essentially concerned with component reliability, while the second part concerns system reliability. Throughout the book the emphasis is on making minimal assumptions, based solely on plausible physical considerations so that the resulting mathematical deductions may be safely made about a large variety of commonly occurring reliability situations. The assumption that the lifetime distributions have monotone failure rate is one of the unifying influences in the author’s attempt to integrate the existing reliability theory.
The mathematical subject rigorously used in the monograph is probability theory and to some extent the idea of total positivity. “Mathematical Theory of Reliability” is one of the finest books in reliability for all times.
Reviewer: S.Chukova (Flint)

62N05 Reliability and life testing
62-02 Research exposition (monographs, survey articles) pertaining to statistics
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
60K10 Applications of renewal theory (reliability, demand theory, etc.)