Maintenance optimization under non-constant probabilities of imperfect inspections

In this research, we study a single-component system that is characterized by three distinct deterioration states, cf. the Delay Time Model: normal, defective, and failed. The system is inspected periodically, and preventive system maintenance is done after a given 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. We present exact cost evaluations for a given maintenance policy, and we compare our model with non-constant probabilities to a model that considers constant probabilities of inspection errors. Our computational study illustrates that the model with constant probabilities may yield, on average, 19% higher costs than the model using non-constant probabilities of inspection errors. These values depend on the chosen parameter values, but still give an indication of how large the difference between both models can be. Finally, we also present an extension in which a reliability constraint (in terms of average failures per time unit) is added to our problem.