Analytical analysis of production lines with parallel machines

This paper presents an approximate decomposition method for the analysis of production lines with multiple stations which consists parallel machines. The machines are unreliable and have exponential operation, failure, and repair processes. Intermediate buffers between different stations are all with finite capacities. First a two-stage analytical model with multiple independent unreliable machines at each stage and one finite-sized buffer between the stages is introduced as the basic component of other building blocks in the system. Then an approximate decomposition method is presented to analyze the system productivity and average work-in-process level. Numerical experiments are given at the end to show the accuracy and efficiency of the decomposition method.