Predicting performance measures for Markovian type of manufacturing systems with product failures

Optoelectronic products are typically assembled and tested in a flow shop environment with multiple processors at each stage. The first few stages are dedicated for assembly and the later stages are dedicated for calibration and testing. Whenever a product (or job) fails at a stage, it is routed back to one of the downstream stages or to the same stage (depending upon the nature of the failure). Consequently, the product could circulate several times between the current stage and the preceding stage(s) before moving to the next stage. Estimating the performance measures (such as WIP and flow time) of such manufacturing systems is not trivial. This paper presents analytical approximations to estimate the performance measures of a manufacturing system with multiple product classes, job circulations due to failures, and some resources being shared among different product classes. The analytical approximations were verified using simulation on several problem instances. The experimental study indicates that these approximations can be used by operations managers to estimate the performance measures of a manufacturing system with product failures.