## The Annals of Probability

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

#### 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

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