The Annals of Probability

On the First Passage Time Distribution for a Class of Markov Chains

Mark Brown and Narasinga R. Chaganty

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Abstract

Consider a stochastically monotone chain with monotone paths on a partially ordered countable set $S$. Let $C$ be an increasing subset of $S$ with finite complement. Then the first passage time from $i \in S$ to $C$ is shown to be IFRA (increasing failure rate on the average). Several applications are presented including coherent systems, shock models, and convolutions of IFRA distributions.

Article information

Source
Ann. Probab., Volume 11, Number 4 (1983), 1000-1008.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993448

Digital Object Identifier
doi:10.1214/aop/1176993448

Mathematical Reviews number (MathSciNet)
MR714962

Zentralblatt MATH identifier
0529.60069

JSTOR
links.jstor.org

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60K10: Applications (reliability, demand theory, etc.)

Keywords
Markov chains first passage times reliability coherent systems shock models multinomial distributions stochastic monotonicity partially ordered sets total positivity IFRA IFR NBU

Citation

Brown, Mark; Chaganty, Narasinga R. On the First Passage Time Distribution for a Class of Markov Chains. Ann. Probab. 11 (1983), no. 4, 1000--1008. doi:10.1214/aop/1176993448. https://projecteuclid.org/euclid.aop/1176993448


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