Elementary methods for failure due to a sequence of Markovian events. (1998)

• Record Type: Journal Article
• Authors: Gani, J.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 11:Number 3(1998)
• Page Start: 311
• Page End: 318
• Publication Date: 1998
• Subjects: failure time -- Markov chain -- augmented transition probability matrix -- sequence overlap -- continuous time; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953398000264
• Languages: English
• ISSNs: 1048-9533

Abstract

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.