Stochastic processes with applications to reliability theory
type: Item
instance of: scholarly article
title: Stochastic processes with applications to reliability theory
zbMATH Open document ID: 1244.60002
DOI: 10.1007/978-0-85729-274-2
author: Toshio Nakagawa
published in: Springer Series in Reliability Engineering
publication date: 2011-02-21T00:00:00Z
review text: The addressed readership of this book is the reliability engineering community, especially engineers looking for a ``book written in an easy style on stochastic processes to be able to understand readily reliability theory''. Chapter headings and some additional remarks: Poisson processes (homogeneous and nonhomogeneous, compound); renewal processes (alternating); Markov chains (discrete- and continuous-time); semi-Markov and Markov renewal processes; cumulative processes (damage models, replacement); Brownian motion and Levy processes (damage models); redundant systems (recalling many of the processes from the previous chapters with a view towards applications). The book can serve as a first attempt to find needed facts in the area of stochastic processes, in my opinion its value lies in the included pointers to more detailed works. It can be recommended as a first step into the field if one needs help on the theory and applications of stochastic processes. Because each chapter includes a substantial list of references, I think it might be helpful in this direction. Nevertheless, the book itself provides many exercises and examples which might be helpful for reliability engineers interested in becoming more familiar with stochastic processes on a level above introductory courses. In my view, there is also another audience for this book: teachers of courses in stochastic processes on an undergraduate or graduate level who want to include examples of applications of stochastic processes in reliability. In this direction, I find this book a valuable source of examples which will be helpful for students, although I would not recommend to use the book as a textbook for such courses.
reviewed by: Hans Daduna
Mathematics Subject Classification ID: 60-01
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 60K20
Mathematics Subject Classification ID: 68M15
Mathematics Subject Classification ID: 90B25
zbMATH DE Number: 5853980
zbMATH Keywords: Poisson processes
zbMATH Keywords: renewal processes
zbMATH Keywords: Markov chains
zbMATH Keywords: semi-Markov and Markov renewal processes
zbMATH Keywords: cumulative processes
zbMATH Keywords: Brownian motion and Levy processes
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-0-85729-274-2
OpenAlex ID: W4249502605
description: scientific article; zbMATH DE number 5853980