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.
Publié le : 1983-11-14
Classification:
Markov chains,
first passage times,
reliability coherent systems,
shock models,
multinomial distributions,
stochastic monotonicity,
partially ordered sets,
total positivity,
IFRA,
IFR,
NBU,
60J10,
60K10
@article{1176993448,
author = {Brown, Mark and Chaganty, Narasinga R.},
title = {On the First Passage Time Distribution for a Class of Markov Chains},
journal = {Ann. Probab.},
volume = {11},
number = {4},
year = {1983},
pages = { 1000-1008},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993448}
}
Brown, Mark; Chaganty, Narasinga R. On the First Passage Time Distribution for a Class of Markov Chains. Ann. Probab., Tome 11 (1983) no. 4, pp. 1000-1008. http://gdmltest.u-ga.fr/item/1176993448/