Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 3, Pages 311-318
doi:10.1155/S1048953398000264
Elementary methods for failure due to a sequence of Markovian events
Australian National University, School of Mathematical Sciences, ACT, Canberra 0200, Australia
Received 1 October 1997; Revised 1 January 1998
Copyright © 1998 J. Gani. 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.
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.