An optimization model of inspection associated with a non-monotonic failure rate model

Reliability-centered maintenance defines a maintenance task called failure-finding task. It actually deals with establishing an inspection schedule for systems that are subject to random failure and where the failure can be detected only through an inspection. The inspection optimization models usually assume that the failure model has an increasing or constant failure rate. However, the failure rate may be non-monotonic. For example, if the failure model follows lognormal distribution, then failure rate is unimodal. This paper presents a three-parameter model to generate the optimal inspection sequence when the failure rate is unimodal.