Models for determining the optimal in-process inspection specification limits in multistage production systems

Abstract

A multistage production system is characterized by items being processed through a sequence of production operations. In general, it may be desirable to have inspection operations performed between some production operations for the purpose of detecting a defective item prior to the final inspection. Furthermore, it may even be more economically desirable to consider tightening the specifications—that is. rejecting a manufacturing unit having defects less than the maximum number to be tolerated. Thus, the hypothesis examined in this paper is that there could exist a method for determination of economically optimal specifications for in-process inspection of a multistage production system. Two production environments considered are: (a) a manufacturer producing to satisfy a fixed production goal, so that any defective item must be replaced by reprocessing a substitute; (b) a manufacturer producing until be exhausts fixed levels of resource availability, so that a rejected item results in a loss in revenue. An economic dynamic programming model is formulated for each of the two production environments. Illustrative examples are presented. Indications are that the concept of specification tightening should be considered for utilization, and that the dynamic programming approach can be used to determine the most economic specification limits for a given inspection program.