On the throughput of deterministic flow lines with random state dependent setups: Stochastic models and applications

Inspired by clustered photolithography tools in semiconductor wafer manufacturing, we study flow lines with deterministic process times subject to random state dependent setups. For tractability, we assume that the setup probability is constant and independent from customer to customer; the setup duration is constant. We show that the internal state of such a flow line can be modeled as a Markov chain when customers arrive in a just-in-time (JIT) fashion. We then develop expressions for the system throughput. We apply our models to clustered photolithography tools and demonstrate how the methods can be used to calculate their capacity.