Decomposition without aggregation for performance approximation in queueing network models of semiconductor manufacturing

Abstract

Accurate and speedy forecasts of production cycle time are key components that support the operation of modern semiconductor wafer fabricators. Estimates of cycle time can be obtained via simulation, but such an approach, though common, requires significant computational investment and model maintenance. Queueing network models and approximations for their performance can provide a viable alternative. As modern semiconductor manufacturing systems exhibit largely reentrant product routing, but contain essential probabilistic routes (for metrology and rework), prior mean cycle time approximation methods are not well suited to the system structure. In this paper, we extend the decomposition without aggregation (DWOA) approach - which is tailored to systems with deterministic routing - to allow for the existence of probabilistic paths. Numerical and simulation studies are conducted with numerous practically inspired datasets to assess the quality of the resulting mean cycle time approximations. The results reveal that our approach outperforms the existing mean cycle time approximations on datasets inspired by the semiconductor industry MIMAC benchmark datasets. For example, in MIMAC dataset 1, our mean cycle time approximations exhibit an average of 10.33% error compared to 18.82% error for existing approaches.