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.
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. https://doi.org/10.1214/aop/1176993448