Optimal Inspection Schedules for Failure Detection in a Model Where Tests Hasten Failures

Methods are well known for determining testing times to minimize the mean cost of testing plus mean cost of an undetected failure (linear in the mean time between failure and detection) when testing does not degrade a good system. Here, we introduce a model in which the ith test increases the remaining failure rate without changing the form of the conditional lifetime distribution. We give algorithms for finding the best testing times in cases of uniform and exponential failure time distributions. Optimization over a single cycle is considered first, and then the case with component renewals is solved using the mean-loss-per-unit-time criterion.