Abstract
It is well-known in the standard age replacement policy that a finite preventive replacement time does not exist when the failure time is exponential and the optimal preventive replacement time is nonrandom. It is shown that when the failure time is exponential, a finite time exists by introducing the shortage and excess costs. In addition, the random age replacement is proposed and similar discussions are made. Furthermore, the periodic and random inspection policies are taken up, and their optimal policies are shown to correspond theoretically to those of the age replacement ones. It is shown finally that when the random inspection cost is the half of the periodic one, two expected costs are almost the same.
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