Periodic Inspection Optimization Models for a Repairable System Subject to Hidden Failures

This paper proposes a model to find an optimal periodic inspection interval over finite and infinite time horizons for a multi-component repairable system subject to hidden failures. The components' failures can only be rectified at periodic inspections, when a failed component is either minimally repaired, or replaced with some age dependent probabilities. We calculate the excepted cost with delayed replacement or minimal repair of a component. Recursive procedures are developed to calculate probabilities of failures in every interval, expected number of minimal repairs, and expected downtimes for optimization over finite and infinite time horizons. Numerical examples of the calculation of the optimal inspection frequencies are given. The data used in the examples is adapted from a hospital's maintenance data for a general infusion pump.