Abstract
Abstract In this paper we consider that a unit is repaired preventively after it has operated for time T . After repair, the unit is not as good as a new one, but is equivalent to one which has been used for a period of time. If we let Y indicate such a period of time, then Y is a random variable related to the time for which the unit has already operated. Hence, under the same repair condition as above, we obtain the unit's renovation degree distribution of Y after the unit is repaired preventively at time kT ( k = 2, 3, … ). Further, using the method of leading variables, we obtain the mean number of times the unit has broken down from time ( k − 1)T to time kT ( k = 1, 2, … ). Finally, considering an objective function with a bound condition and using the Lagrange multipliers method, we obtain an optimal preventive maintenance time T , for which the minimum total repair cost is achieved.
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