## The Annals of Probability

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

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

Mark Brown and Narasinga R. Chaganty

#### 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