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Basic Stochastic Process Theory

  • Alessandro Birolini

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.

Keywords

Markov Process Renewal Process Sojourn Time Embed Markov Chain Active Redundancy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Alessandro Birolini
    • 1
  1. 1.ETH ZurichLuganoSwitzerland

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