Optimal lot size and offline inspection policy

In this study, we investigate the effects of using process status at the end of the production lot (PSPL), on determining the optimal policies for products inspection and production lot size. First, we obtain the optimal product inspection policies for different PSPL for a given lot in the in-control or out-of-control state. Properties for the inspection policy are explored. Then, the expected total cost function, which includes setup cost, process maintenance cost and quality-related control cost, is obtained. The optimal production lot size that minimizes the expected total cost per item is determined. Our proposed inspection policy is compared with the three policies of no inspection, full inspection, and disregarding the first s items policy, in which only items from s+1 until the end of the production lot are inspected. Differences in the minimum expected total cost per item between our proposed inspection policy and the other three policies are investigated with a numerical example.