Predicting Cycle Time Distributions for Integrated Processing Workstations: An Aggregate Modeling Approach

Abstract

Predicting the cycle time distribution as a function of throughput is helpful in making a trade-off between workstation productivity and meeting due dates. To predict cycle time distributions, detailed models are almost exclusively used, which require considerable development and maintenance effort. Instead, we propose a so-called aggregate model to predict cycle time distributions, which is a lumped-parameter representation of the queueing system. The lumped parameters of the model are determined directly from arrival and departure events measured at the workstation. The paper demonstrates that the aggregate model can accurately predict the cycle time distribution of workstations in semiconductor manufacturing, in particular the tail of the distribution.

The correct level of model complexity in semiconductor fab simulation — Lessons learned from practice

“…Finally, [35] describes a method for developing an independent queuing theory meta-model for the prediction of fab cycle times by evaluating a limited set of simulation runs, for more contributions regarding meta-models see also [32], [36], [37]. [38] presents an aggregate modeling method for semiconductor workstations in order to predict cycle time distributions. Their aggregate model is a single-server representation of the workstation and shows a good accuracy concerning the prediction of mean cycle time and the 95 % quantile of cycle time distribution.…”

Performance analysis and optimization of queueing network production systems considering non-conforming products rework and departure

“…Performance analysis and optimization problems in queueing systems have received considerable attention in recent years, due to their wide applicability in the performance evaluation and optimal design of manufacturing systems and computer networks (Song et al, 1998). Now, the long serial lines analysis and optimization have been well studied using decomposition (Shi and Gershwin, 2014;Damodaran and Hulett, 2012;Cauffriez and Willaeys, 2006) or aggregation (Veeger et al, 2011;Belmansour and Nourelfath, 2008) methods for a long time, and extensive results are obtained. Although many studies have focused on solving the line optimization problems, the studies in which a large number of approaches are currently applied to research the performance of queueing network systems considering the non-conforming products are still extremely limited.…”

Conditional inter-departure times from the M/G/s queue

“…Our interest in conditional inter-departure times arose out of work on aggregate modeling of multi-processing work stations, where the conditional inter-departure times are treated as work-in-process dependent process times in the aggregate model; see [4,7,8].…”