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**Stochastic processes and reliability of systems.
(Processus stochastiques et fiabilité des systèmes.)**
*(French)*
Zbl 0883.60002

Mathématiques & Applications (Berlin) 28. Berlin: Springer. xiii, 435 p. (1997).

Prepared for advanced undergraduate-graduate courses, this theoretically oriented textbook integrates mathematical/statistical results on stochastic processes with basic elements of systems reliability. Its aim is to show the benefice of using stochastic processes in this applied field. The book starts with a preliminary chapter devoted to the fundamental reliability notions (Chapter 1). The remaining text is divided into two parts which are more or less independent. Part I concerns statistical analysis of failures. The chapters included are paired: Poisson processes (Chapter 2) and Poisson processes and reliability (Chapter 3); point processes and martingales (Chapter 4) and point processes and reliability (Chapter 5). In Part II renewal theory is essentially used; an entire chapter (Chapter 6) is devoted to it. Next, the following subjects are dealt with: some models for systems structure (Chapter 7), Markov jump processes (Chapter 8), Markov processes and reliability (Chapter 9), semi-Markov processes (Chapter 10). A very few number of exercises are accompanying each chapter.

The book presupposes a very good knowledge of probability and statistics. In this sense seven appendices, added at the end of the text, may help out the reader. In conclusion, a useful addition to the literature written in French on stochastic processes and reliability.

The book presupposes a very good knowledge of probability and statistics. In this sense seven appendices, added at the end of the text, may help out the reader. In conclusion, a useful addition to the literature written in French on stochastic processes and reliability.

Reviewer: R.Theodorescu (Quebec)

### MSC:

60-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory |

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

60J75 | Jump processes (MSC2010) |

60G55 | Point processes (e.g., Poisson, Cox, Hawkes processes) |

90-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming |