Open Access
November, 1983 On the First Passage Time Distribution for a Class of Markov Chains
Mark Brown, Narasinga R. Chaganty
Ann. Probab. 11(4): 1000-1008 (November, 1983). DOI: 10.1214/aop/1176993448


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.


Download Citation

Mark Brown. Narasinga R. Chaganty. "On the First Passage Time Distribution for a Class of Markov Chains." Ann. Probab. 11 (4) 1000 - 1008, November, 1983.


Published: November, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0529.60069
MathSciNet: MR714962
Digital Object Identifier: 10.1214/aop/1176993448

Primary: 60J10
Secondary: 60K10

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

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 4 • November, 1983
Back to Top