Abstract
We consider a system that gradually deteriorates. At random times Tn the system is inspected and may or may not be replaced, but it must be if its state is too bad. The process of deterioration is described by a Markovian renewal process. Under some monotonicity conditions we derive a policy for the finite and the infinite horizon which minimizes the total discounted costs. This paper is a generalization of a result of Feldman (1977).
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