(An) improved cost limit replacement policy under minimal repair

Abstract

This thesis presents an improved cost limit replacement policy under minimal repair. When a system requires repair, it is first inspected and the repair cost is estimated. Specifically, the policy prescribes the allowed number of repairs of which the cost exceeds a certain amount known as the "repair limit", before replacement. Then, the failed system is minimally repaired either if the repair cost is estimated to be less than the cost limit or if the number of repairs of which the cost exceeds the cost limit is less than the prescribed one. Otherwise the failed one is replaced by a new one. A Weibull failure distribution and a Negative exponential repair cost distribution are assumed for analytic tractability. The average cost per unit time for repairs and replacement over an infinite horizon is applied as a criterion, and the optimal policy is developed to minimize it. It is shown that the optimal policy is unique and finite.