Letter to the Editor—Nonoptimality of Planned Replacement in Intervals of Decreasing Failure Rate

Abstract

The planned replacement problem assumes a known failure distribution F ( t ) and that replacement occurs at the earlier of a planned replacement interval (at cost c 1 ) and the time of failure (at cost c 2 ). We show that it cannot be optimal to select a planned replacement interval at a point for which the failure rate f ( t )/[1 − F ( t )] is decreasing.