Annals of Probability
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 ∈ S to C is shown to be IFRA (increasing failure rate on the,av;rage). Several applications are presented including coherent systems, shock models, and convolutions of IFRA distributions.
Original Publication Citation
Brown, M., & Chaganty, N. R. (1983). On the first passage time distribution for a class of Markov chains. Annals of Probability, 11(4), 1000-1008. doi:10.1214/aop/1176993448
Brown, Mark and Chaganty, Narasinga Rao, "On the First Passage Time Distribution for a Class of Markov Chains" (1983). Mathematics & Statistics Faculty Publications. 166.