Description:
<jats:p>We consider a system that gradually deteriorates. At random times <jats:italic>T<jats:sub>n</jats:sub>
</jats:italic> 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).</jats:p>