Performance evaluation and design of a constant work-in-process system with inspections

In this paper, we analyze a CONWIP (Constant Work-In-Process) system which consists of three stations in series. We assume that raw parts are always available. When a finished part is consumed by a demand, a raw part is released immediately and gets processed at each station sequentially. The processings do not always meet the requirement of quality. Therefore, at the end of the processing at each station, a part is inspected randomly to determine if it satisfies the requirement of quality. We assume that the inspection time is negligible. If a part is inspected and found to be defective because of treatment at station j, the part is fed back to station j to be treated again. We consider that the stations have an exponential or an N-stage Coxian service time distribution. We propose an analytical method to evaluate the performance of this kind of system. We consider two cases: one is the saturated case where the supply of demands is infinite and the other is the non-saturated case where external demands arrive according to a Poisson process. Then we use the analytical method to show how the optimal CONWIP system can be designed for a chosen design criterion. Although we present the method only for three-station systems in this paper, it can be easily extended to systems with more than three stations.