An optimal maintenance (during operation) and overhaul (repair) policy is derived for a production machine. The problem is formulated as a 2-state semi-Markov decision process. If the machine fails during operation, it then transits to the overhaul state. If the machine does not fail, it will become imperative to overhaul it due to increasing maintenance cost.
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Khandelwal et al. (1979) studied this question.
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