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

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 c₁) and the time of failure (at cost c₂). 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.