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

Cocozza-Thivent, Christiane

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.

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

Keywords:

stochastic processes; Markov processes; point processes; martingales; reliability; systems theory; failure; textbook