Optimal inspection schedule in an imperfect EMQ model with free repair warranty policy

The paper considers a sequential inspection policy in an imperfect production process which shifts randomly from an 'in-control' state to an 'out-of-control' state following a general probability distribution. Two different inspection policies are adopted in the proposed model: (i) no action is taken in the intermediate of a production run unless the process is found in an 'out-of-control' state by inspection and (ii) preventive repair action is undertaken once the 'in-control' state of the process is detected by inspection. The manufacturer is in a contractual agreement with the customer to provide free minimal repair service until a certain (warranty) period from the time of initial purchase. The objective is to determine the optimal number of inspections and inspection time sequence during a production run which minimize the manufacturer's future expected costs in present term or average cost in distant future. The proposed model is formulated under discounted as well as long-run average cost criteria and some structural properties on the optimal inspection policy are derived analytically. For a numerical example, the optimal inspection policy is determined and several managerial insights are investigated.