The reliability of a large series system under Markov structure

Let Y 1, · ··, Yn be a finite Markov chain and let f be a binary value function defined over the state space of the Y's. We study the reliability of general series system having the structure function φ (Y) = min {f(Y 1), · ··, f(Yn )} and show that, under certain regularity conditions, the reliability of the system tends to a constant c (1 ≥ c ≥ 0), where c often has the form c = exp {–λ}.