An inspection model of products and their input materials

Consider an input material with a nonconforming probability that is used for the production of a product through a deteriorating process, which is initially maintained in an in-control state, but can randomly shift into an out-of-control state after some products are produced. To economically control the total quality-related cost for a given production lot, an optimal inspection policy for the products and their input materials is proposed. Furthermore, under the optimal inspection policy, a decision on the optimal production lot size is also incorporated. The unique properties and conditions that give the optimal production lot size are explored. Numerical examples are given to illustrate our proposed inspection and production model. The effects of the model's parameter values, such as inspection error rate, unit inspection cost for the input material, unit inspection cost for the product, etc., on the optimal solution are investigated. Finally, some useful insights that should help industrial operations are presented.