The reliability of a large series system under Markov structure

Let Y, - -, Y,, 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 op(Y) = min {f(Y1), - -, f(Y,)} 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 {-,A}.