Maintenance optimization under non-constant probabilities of imperfect inspections

In this research, we study a single-component system that is characterized by three distinct states, cf. the Delay Time Model: normal, defective, and failed. The system is maintained by an inspection policy with fixed time intervals, and preventive system replacement after a number of inspections. The inspections are imperfect, and the probability of an inspection error changes over the system’s operation time. Our objective is to minimize the average cost over an infinite time horizon, under a reliability constraint. We present exact cost and reliability evaluations under a given maintenance policy, for a model considering non-constant probabilities of inspection errors. We call this model the true model. Furthermore, we compare the true model to a model that considers constant probabilities of inspection errors. We refer to this latter model as the approximate model. By means of a computational study, we find that the approximate model yields, on average, 26% higher costs than the true model. Furthermore, we find that the reliability constraint can be violated severely, by at most 25%, when using the approximate model.