Maintenance modelling of a multi-state critical system subject to inspection defaults and errors

Abstract This study develops a maintenance policy that integrates inspections and preventive replacement and that is specifically designed for systems with three distinct stages of degradation. The proposed approach distinguishes itself from previous models by accounting for: external factors that may impede the execution of inspections; inspection errors such as false negatives and defect induction. A key innovation of this model is the incorporation of the concept of default, which represents the probability of not performing an inspection as scheduled. This is critical because it directly impacts the recognition of defective states (minor and major) that serve as opportunities to prevent failure. An objective function is formulated to minimize the long-run cost-rate, modelled using Renewal-Reward Theory. The modelling is motivated by maintenance of a CNC machine. Sensitivity analysis shows that defect induction and defaults significantly reduce the number of inspections suggested by the model, highlighting the importance of improving inspection quality to prevent defect induction. The ”cost of ignorance” that relates to the model’s parameters is estimated as 7.2%, thus reinforcing the effectiveness of the model. Finally, to support maintainers, we have developed a user-friendly web application.