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This paper treats an optimal inspection and maintenance policy of a continuous time Markovian deteriorating system, which minimizes the total discounted expected time in which the system is not operating. The problem is formulated by a semi-Markov decision process and some properties of an optimal policy are obtained, that is, a control limit rule holds and as the system degrades, an optimal inspection time interval becomes shorter. For a discrete time Markovian deterioration case, almost the same discussion is made.
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Mine et al. (1982) studied this question.
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