Preventive replacement for systems with condition monitoring and additional manual inspections

Condition monitoring (CM) and manual inspection are increasingly used in industry to identify a system's state so that necessary preventive maintenance (PM) decisions can be made. In this paper, we present a model that considers a single-unit system subject to both CM and additional manual inspections. There are two preset control limits: an inspection threshold and a preventive replacement (PR) threshold. When a CM measurement is equal to or greater than the inspection threshold but is less than the PR threshold, a manual inspection activity is initiated. When a CM measurement is greater than the PR threshold, a PR activity should be carried out. The system's degradation process evolves according to a two-stage failure process: the normal working stage, which is from new to the initial point that a defect occurs, with the CM measurement coming from a stochastic process; and the delay-time stage, which is from the initial point that a defect occurs until the point of failure, with the CM measurement coming from an increasing stochastic process. We assume that a manual inspection is perfect in that it can always identify which of these two stages the system is in. In our study, the decision variables are the CM interval and the inspection threshold, and we aim to minimize the expected cost per unit time. We provide a numerical example to demonstrate the applicability and solution procedure of the model.