Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 3, Pages 311-318
doi:10.1155/S1048953398000264
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.