Abstract
The optimal minimal-repair and replacement problem of a reliability system under the average cost criterion is formulated as a semi-Markov decision process. It is assumed that the cost structure of the system depends on its age. Under some weak assumptions, it is shown that, among all allowable policies, an optimal policy is a t-policy. That is, failures before age t are minimally repaired, but the system is replaced when a failure after age t occurs.
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