Optimum inspection interval for a system under periodic and opportunistic inspections

This article proposes a model to find an optimal periodic inspection interval over a finite time horizon for a multi-component system. The system's components are subject to either hard or soft failures. Hard failures are detected and fixed instantaneously. Soft failures are unrevealed and can only be detected at inspections. Soft failures do not stop the system from operating; however, they may reduce its level of performance from its designed value. The system is inspected periodically to detect soft failures; however, a hard failure instance also provides an opportunity called opportunistic inspection to inspect and fix soft failures. Two models are discussed in this article. The first model assumes that components with soft and hard failures are minimally repaired. The second model assumes the possibility of either minimal repair or replacement of a component with soft failure, with some age-dependent probabilities. Recursive procedures are developed to calculate the expected number of minimal repairs and replacements and expected downtimes of components with soft failure. Examples of the calculation of the optimal inspection intervals are given. The data used in the examples are adapted from a hospital's maintenance data for general infusion pump.