In this paper we consider an infinitely deep dam fed by inputs which form an ergodic Markov chain and whose release M is non-unit. The extension to non-unit release follows on lines similar to the independent inputs case. We show that P(θ) – θ MΙ where P(θ) = (pijθ i) has a maximum of N = M(M + l)/2 non-zero singularities in the unit disc, so that the general solution of the equilibrium equations has N unknown constants. We also show that these constants satisfy N linear constraints, so that the solution is fully determined.

We have recently discussed the replacement problem of a parallel system in a random environment. This paper extends the same replacement problem for the following two cases which are more plausible: (i) The probability that an operating component fails by the j th shock depends on the number j. (ii) The replacement cost is a linear function of failed components. The expected cost of the above model is obtained. A numerical example is finally presented when the probability of failure time of a component is a negative binomial distribution.