Modelling imperfect inspection over a finite horizon

This paper models imperfect inspection policies for a system with a finite operational time requirement. Two types of maintenance policy are considered: that in which an alarm (a positive inspection) is followed by a check of the validity of the alarm at additional cost, and if the system is good it continues in service and if failed it is retired; and that in which a positive inspection leads to retirement of the system regardless of the true system state. False negative inspections may also occur. The cost implications and applicability of these policies are different, but the mathematical analyses of the models are related. We also allow aperiodic inspection. The models we describe are general and allow one to explore maintenance planning options for systems that are close to retirement.