A sequential inspection and preventive replacement policy for heterogeneous components

In this study, some rigid assumptions of models that establish inspections at constant intervals (periodic or non-sequential) are relaxed. A new hybrid policy of sequential inspections and preventive replacement is proposed. The proposed model, based on the delay-time concept and calculated using the renewal theory with rewards, is designed for a single-component system, where the components come from a heterogeneous population (weak and strong). The model is also extended to consider imperfect inspections (false positives and negatives), addressing the misclassification of defects, a common issue in practice. The proposed policy is compared with two other classic policies from the literature: a hybrid policy of non-sequential inspections and preventive replacement, and a pure inspection policy. The long-term cost rate per unit of time is calculated, and the numerical results demonstrate savings of up to 6.4%, especially when the costs in the defective state are high.