A device is subject to damage. The damage occurs randomly in discrete timeaccording to an increasing homogeneous Markov chain, where the incremental damagecaused by a shock depends on the magnitude of the shock. The device has a threshold,and it fails once the damage level exceeds the threshold. Upon failure the device is replacedby a new and identical one and a cost is incurred. If the device is replaced before failure,a smaller cost is incurred. In this paper we study the problem of specifying a replacementrule which minimizes the long-run (expected) average cost per unit time. Under mildconditions we show that the optimal replacement policy exists and it possesses the controllimit property.
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