An inspection policy for a stochastically failing single-unit system

Inspection is considered as a means of confirming whether maintenance-intended equipment operates normally or whether it works correctly when required for operation. Inspection costs increase when the inspection interval is shortened since inspection is one of the cost elements. On the contrary, risk or loss caused by failure will increase when the inspection interval is lengthened. Therefore, an appropriate setting of inspection schedules is important for reduction in maintenance costs. In this study, a determination method optimum inspection schedules is discussed for a single-unit system, in which failure of a system is detected only by inspection. An optimization problem is formulated to minimize the incurred cost per cycle in order to derive an optimum inspection density function, in which the problem is solved by the variational method.