Application of Erlang distribution in cycle time estimation of toolsets with wip-dependent arrival and service in a single product-type single failure-type environment

This paper proposes a methodology based on phase type distributions and a state dependent Markov chain model to estimate the cycle time of workstations (toolsets) in semiconductor manufacturing. Due to implicit operational policies adopted by the line managers the performance of the existing queueing models for toolsets is not satisfactory. On the other hand developing accurate simulation models for toolsets can be very time consuming and hard to maintain. In this paper we propose a Markov chain model with the ability to include implicit operational rules on dispatching and maintenance. We verify the performance of this model via simulation and present the results for a variety of arrival and service distribution shapes.