The throughput rate of serial production lines with deterministic process times and random setups: Markovian models and applications to semiconductor manufacturing

Abstract

We conduct exact analysis of serial production lines with deterministic service durations and various classes of random state-dependent setups between customers. Our focus is on assessing the production rate, or just-in-time (JIT) throughput. We demonstrate that such systems can be modeled as a Markov chain and consider various types of setups inspired by clustered photolithography tools in semiconductor manufacturing. We deduce when exact closed form expressions for the production rate are possible and when a numeric solution to the Markov chain balance equations are required. As these systems have shown promise for modeling process bound clustered photolithography tools, we study their accuracy versus detailed simulation for predicting the tool throughput. Various practical features such as the capacity of a pre-scan buffer and batch customers (to model wafer lots) are investigated.