Performance characterization of complex manufacturing systems with general distributions and job failures

In optoelectronics assembly, the first few stages of the assembly line are dedicated to build the product and the later stages are dedicated for calibration and testing. The assembly line is arranged in a flow shop environment with multiple processors at each stage. When a product (or job) fails at a stage, it is routed back to one of the previous stages or to the same stage (depending upon the nature of the failure). Consequently, the product could circulate between the current stage and the previous stage(s) before it is transferred to the next stage. Estimating the performance measures of such complex manufacturing systems, while considering multiple product classes, random job failures, and resource sharing, is not trivial. This paper presents the approximations used to estimate the performance measures of such complex manufacturing systems with general arrival and service distributions. The analytical approximations have been validated using discrete event simulation and the source of error between them is identified. These approximations can be used by operations managers to estimate the performance measures such as WIP and flow time.