International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 1998 / Article

Open Access

Volume 11 |Article ID 947340 | 8 pages | https://doi.org/10.1155/S1048953398000264

Elementary methods for failure due to a sequence of Markovian events

Received01 Oct 1997
Revised01 Jan 1998

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.

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.

46 Views | 246 Downloads | 1 Citation
 PDF  Download Citation  Citation
 Order printed copiesOrder

We are committed to sharing findings related to COVID-19 as quickly and safely as possible. Any author submitting a COVID-19 paper should notify us at help@hindawi.com to ensure their research is fast-tracked and made available on a preprint server as soon as possible. We will be providing unlimited waivers of publication charges for accepted articles related to COVID-19. Sign up here as a reviewer to help fast-track new submissions.