A new aggregation algorithm for performance metric calculation in serial production lines with exponential machines: design, accuracy and robustness

Performance metric calculation is one of the most important problems in production system research. In this paper, we consider serial production lines with finite buffers and machines following the exponential reliability model. Analytical formulas are first given for performance analysis of two-machine lines. Based on these formulas, a throughput-equivalent aggregation procedure is derived to represent a two-machine exponential line by a single exponential machine. Following this approach, we propose a new aggregation-based iterative algorithm to calculate the performance metrics of a multi-machine serial line by representing it using a group of virtual two-machine lines. Numerical experiments are used to justify the convergence of the algorithm and to evaluate the accuracy of the calculated performance metrics. The results show that the proposed algorithm significantly improves the performance metric approximation accuracy, compared with two commonly used aggregation-based methods in the literature, without incurring additional computational burden. The improvement is even more prominent for systems with relatively small buffers. We believe that this work makes an important contribution to the field of Production Systems Engineering and has the potential to generate great impact as the new algorithm replaces the existing ones in future research and applications by scholars and practitioners.