Performance analysis in a re-entrant operation with combinational routing and yield probabilities

Queuing networks arising from multistage processes with probabilistic re-entrant lines are common in manufacturing environments. Probabilistic re-entrant operation is defined as lots entering the operation with different repeated cycle requirements. This paper extends our work [S. Kumar, M.K. Omar, Stochastic re-entrant line modeling for an environmental stress testing in a semiconductor assembly industry, Appl. Math. Comput. 173 (2006) 603–615.] and proposes a modified analytical method based on the mean value analysis (MVA) technique and considering a probabilistic re-entrant line with yield loss probabilities. Introducing probabilities consideration into the MVA approach will substantially increase the complexity of the modeling and results analysis. However, the contribution of this paper is the introduction of a solution methodology that can overcome such complexity and allow operational managers to compute performance measures such as total cycle time and the mean throughput.Moreover, our paper presents numerical tests under various probabilistic re-entrant and yield conditions to show the performance of the proposed approach compared with results obtained from a simulation model developed by the authors.