Integrated production and product inspection policy for a deteriorating production system

A production system subject to random deterioration from the in-control state to the out-of-control state produces more defective items in the out-of-control state. In the literature, full inspection policy is considered so that all the defective items can be eliminated; however, it incurs higher inspection costs. In this study, instead of full inspection, product inspections are performed only at the end of the production run. A mathematical formula representing the expected total cost per item is derived for a deteriorating process, where the in-control period follows a general probability distribution. Our objective here is the joint optimization of the production run length and product inspection policy, aiming to minimize the expected total cost per item. Since there is no closed form expression for the optimal production/inspection (PI) policy, some useful properties are obtained to establish an efficient solution procedure for the optimal PI policy. In the exponential case, an approximate solution for the optimal PI policy is derived. Numerical examples are given to illustrate the PI model. The numerical examples show that such PI model will reduce the quality-related cost than full inspection does.