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Basic Stochastic Process Theory

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Reliability Engineering

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Abstract

Stochastic processes are powerful tools for the investigation of the reliability and availability of repairable equipment and systems. They can be considered as families of time-dependent random variables or as random functions in time, and thus have a theoretical foundation based on probability theory (Appendix A6). The use of stochastic processes allows the analysis of the influence of the failure-free operating and repair time distributions of elements, as well as of the system’s structure, repair strategy, and logistical support, on the reliability and availability of a given system. Considering the applications given in Chapter 6, and for reasons of mathematical tractability, this appendix mainly deals with regenerative stochastic processes with a finite state space, to which belong renewal processes, Markov processes, semi-Markov processes, and semi-regenerative processes. The theoretical presentation will be supported by examples taken from practical applications. This appendix is a compendium of the theory of stochastic processes, consistent from a mathematical point of view but still with engineering applications in mind.

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Authors and Affiliations

  1. ETH Zurich, Via Generoso 5, 6900, Lugano, Switzerland

    Prof. Dr. Alessandro Birolini (emerit. o. Prof.)

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  1. Prof. Dr. Alessandro Birolini
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© 1999 Springer-Verlag Berlin Heidelberg

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Birolini, A. (1999). Basic Stochastic Process Theory. In: Reliability Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03792-8_15

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  • DOI: https://doi.org/10.1007/978-3-662-03792-8_15

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  • Print ISBN: 978-3-662-03794-2

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