Product inspection policy for an imperfect production system with inspection errors and warranty cost

•Product inspection policy is considered.•Two types of inspection errors namely Type I error and Type II error are introduced.•Warranty cost is assumed for non-inspected items.

During manufacturing of products, all produced items are considered as perfect in general. This viewpoint of taking all finished products are perfect is not correct always. Defective items may occur during the production process for several reasons. This paper describes a deteriorating production process which randomly shifts to out-of-control state from in-control state. In case of full inspection policy, expected total cost together with inspection cost results higher inventory cost. Therefore, product inspection policy is better to use for reducing inspection costs. During product inspection process, inspectors may choose falsely a defective item as non-defective and vice-versa. Type I and Type II errors are incorporated in this model to make more realistic rather than existing models. This model includes a warranty policy for some fixed time periods. Some numerical examples, sensitivity analysis, and graphical representations are given to illustrate this model.