Semi-Markov Processes and Reliability

  • N. Limnios
  • G. Oprişan

Part of the Statistics for Industry and Technology book series (SIT)

Table of contents

  1. Front Matter
    Pages i-xii
  2. N. Limnios, G. Oprişan
    Pages 31-49
  3. N. Limnios, G. Oprişan
    Pages 51-83
  4. N. Limnios, G. Oprişan
    Pages 121-151
  5. N. Limnios, G. Oprişan
    Pages 153-176
  6. Back Matter
    Pages 177-222

About this book

Introduction

At first there was the Markov property. The theory of stochastic processes, which can be considered as an exten­ sion of probability theory, allows the modeling of the evolution of systems through the time. It cannot be properly understood just as pure mathemat­ ics, separated from the body of experience and examples that have brought it to life. The theory of stochastic processes entered a period of intensive develop­ ment, which is not finished yet, when the idea of the Markov property was brought in. Not even a serious study of the renewal processes is possible without using the strong tool of Markov processes. The modern theory of Markov processes has its origins in the studies by A. A: Markov (1856-1922) of sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian mo­ tion. Later, many generalizations (in fact all kinds of weakenings of the Markov property) of Markov type stochastic processes were proposed. Some of them have led to new classes of stochastic processes and useful applications. Let us mention some of them: systems with complete connections [90, 91, 45, 86]; K-dependent Markov processes [44]; semi-Markov processes, and so forth. The semi-Markov processes generalize the renewal processes as well as the Markov jump processes and have numerous applications, especially in relia­ bility.

Keywords

Brownian motion Engineering reliability Markov Markov kernel Markov process Simulation Stochastic processes algorithm algorithms data analysis modeling probability theory risk engineering statistics stochastic process

Authors and affiliations

  • N. Limnios
    • 1
  • G. Oprişan
    • 2
  1. 1.Division Mathématiques AppliquéesUniversité de Technologie de CompiègneCompiègne CedexFrance
  2. 2.University of “Politehnica” of Bucharest 313BucharestRomania

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0161-8
  • Copyright Information Birkhäuser Boston 2001
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6640-2
  • Online ISBN 978-1-4612-0161-8
  • About this book