Optimal Replacement Age in an Imperfect Inspection Model

摘要

A device is maintained under an age replacement policy. The status of the device (functioning or failed) is known only by inspection at some fixed interval k. With probability q, an inspection error may be made, and a functioning unit will be declared to have failed and be replaced by a new unit. On the contrary, when a failed unit is inspected, it is assumed that no inspection error will be made. Assuming that the cost of replacing a failed unit (actually failed or believed failed) is greater than the cost of replacing a functioning unit, we show that we can obtain an optimum replacement age which minimizes L(T), the long-run expected cost per unit of time. We find a lower bound for the optimal replacement age and obtain asymptotic and monotonicity properties for L(T). (Author)