Elementary methods for failure due to a sequence of Markovian events

[摘要] 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 timeTto failure can be obtained from the probability generating function (p.g.f.) ofT. The method can be extended to the case of continuous time.

[学科分类] 应用数学