Optimal buffer inventory and inspection errors in an imperfect production system with preventive maintenance

This paper considers an imperfect production system with preventive maintenance to obtain the optimal buffer inventory and inspection policy for sold products with free minimal repair warranty. The production system is subject to a random movement from an in-control to an out-of-control state, where some proportion of defective items are produced by the production system during both the in-control and out-of-control states. Online inspection is continuing after a time variable during the production process. Another offline human-based inspection policy is considered at the end of the production cycle to identify the defective items. Defective items found by the inspector are salvaged at some fixed cost before being shipped and the non-inspected items are passed to the customer with free minimal repair warranty. During human-based inspection, some misclassifications may arise from the inspector's side. Thus, two types of inspection errors (Type I and Type II) are considered to make the model more realistic rather than the existing models. A numerical example along with graphical representations are provided to illustrate the proposed model. Sensitivity analysis of the optimal solution with respect to major parameters of the system has been carried out, and the implications are discussed.