Stochastic processes and reliability of systems
type: Item
instance of: scholarly article
title: Stochastic processes and reliability of systems
zbMATH Open document ID: 0883.60002
author: Christiane Cocozza-Thivent
published in: Mathématiques \& Applications (Berlin)
publication date: 1997-10-22T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60-01
Mathematics Subject Classification ID: 90B25
Mathematics Subject Classification ID: 60J75
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 90-01
zbMATH DE Number: 1077342
zbMATH Keywords: stochastic processes
zbMATH Keywords: Markov processes
zbMATH Keywords: point processes
zbMATH Keywords: martingales
zbMATH Keywords: reliability
zbMATH Keywords: systems theory
zbMATH Keywords: failure
zbMATH Keywords: textbook
reviewed by: Radu Theodorescu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1077342