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Elementary methods for failure due to a sequence of Markovian events

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  • J. Gani

Abstract

This paper is concerned with elementary methods for evaluating the distribution of the time to system failure, following a particular sequence of events from a Markov chain. After discussing a simple example in which a specific sequence from a two-state Markov chain leads to failure, the method is generalized to a sequence from a ( k > 2 ) -state chain. The expectation and variance of the time T to failure can be obtained from the probability generating function (p.g.f.) of T . The method can be extended to the case of continuous time.

Suggested Citation

  • J. Gani, 1998. "Elementary methods for failure due to a sequence of Markovian events," International Journal of Stochastic Analysis, Hindawi, vol. 11, pages 1-8, January.
    • Handle: RePEc:hin:jnijsa:947340
    DOI: 10.1155/S1048953398000264
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