Inspection stations are now an integral part of any manufacturing system and help track product quality and process performance. In this paper the authors consider re-entrant manufacturing systems (such as semiconductor fabrication facilities) 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. The authors propose re-entrant lines with probabilistic routing as models for such systems and present an efficient analytical technique based on mean value analysis to predict mean cycle times and throughput rates. The method can be used to compare different ways of locating inspection stations, from a cycle time and throughput viewpoint.