International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1998 / Article

Open Access

Volume 11 |Article ID 947340 | 8 pages |

Elementary methods for failure due to a sequence of Markovian events

Received01 Oct 1997
Revised01 Jan 1998


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.

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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