An inspection and production model with inspection errors

When product inspection time is non-negligible, a previous paper developed an online inspection and production model in which inspection errors do not exist. It is assumed that the inspection rate is less than the production rate, to have an economic production lot size, product inspection information needs to be used to infer process quality so that the quality of the uninspected products can be inferred. Once the expected total cost per conforming product for an evaluated production quantity starts to increase, then production is ceased. However, since inspection itself is imperfect in practice, type I and type II inspection errors exist in reality. Thus, in this paper we have reformulated the previous production and inspection model and incorporated these two types of inspection error with the aim of determining their effect on the optimal production lot size. Illustrative numerical examples are provided to demonstrate the effect of inspection errors on optimal production and on inspection policy.