Modeling reentrant manufacturing systems with inspection stations

Inspection stations are now an integral part of any manufacturing system and help track product quality and process performance. This paper considers reentrant manufacturing systems-such as semiconductor wafer fabrication systems-with inspections at various stages of processing. At the end of each inspection, three possibilities are assumed, namely accept, reject, or rework at some previous stage. Proposed are reentrant lines with probabilistic routing as models for such systems and presented is an efficient, approximate analytical technique based on mean value analysis to predict mean steady-state cycle times and throughput rates. The proposed method explicitly models scheduling policies used in reentrant lines and can be used for rapid performance analysis. Two applications of the analysis methodology are presented. First, it is shown how to compare alternative ways of locating inspection stations from a cycle time and throughput viewpoint. Next, by considering a realistic model of a wafer fab, evaluation is made of the effect of congestion at an inspection station on the cycle time and throughput of the wafer fab.