Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 3, Pages 311-318

Elementary methods for failure due to a sequence of Markovian events

J. Gani

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.


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.