A Markov Chain Framework for Approximation of Cycle Time in Semiconductor Manufacturing Toolsets

Accurate and efficient cycle time approximation is a critical issue in semiconductor manufacturing systems (SMS), since it facilitates the subsequent production planning and scheduling activities and helps reduce the overall cycle time. Presently computer simulation is a common approach to cycle time approximation and performance analysis in SMS. Simulation models however, have several inherent short-comings, and it can be difficult and time-consuming to use such models to explore various what-if questions. Compared with simulation models, analytical approaches based on queuing theory can be much faster in achieving reasonable results, and they typically provide more insights for performance improvement. But in the context of the SMS, performance of the queuing models has not been satisfactory due to inaccurate results.;We believe that a major cause of this poor performance is the application of operational rules in SMS. These rules are typically invented by line managers so as to interfere with various components of the system such as the arrival process, the service process, and the repair process, in an attempt to increase the speed of the production flow. Deployment of such rules, however, creates dependencies among these components of the system which are typically not captured by classical queuing models. This, in turn, could render the results obtained via these models somewhat inaccurate and unsatisfactory.;In this dissertation we propose a Markov chain framework to model the behavior of a toolset (workstation) in SMS under various operational rules, and employ this model to approximate, with a relatively high degree of accuracy, the long-run average cycle-time of jobs at the toolset.;To this end, we first develop a basic state-dependent Markov chain model for an SMS toolset. In this model we assume that all random components of the system, i.e., the inter-arrival time, the service time, the time between failures, and the repair time, are exponentially distributed. The state of this model is defined by a two dimensional vector consisting of the current number of active servers and the WIP level in the toolset, and the transition rates between the states are determined based on the operational rules adopted for the workstation. Given the transition rates we solve the balance equations of the Markov chain to calculate the steady state probabilities for this system. We then use these steady state probabilities to calculate the expected value of WIP for the system, and employ Little's law to determine the long-run average cycle time for the workstation.;Subsequently we extend this Markov chain model to develop a framework for modeling toolsets with other underlying conditions and assumptions. The scenarios that we consider include toolsets with non-exponential distributions for the arrival and the service processes, toolsets with heterogeneous servers, and servers that are prone to multiple types of failure.;In order to evaluate the accuracy of this approach, we conduct a comprehensive computational experiment in which we compare the numeric values obtained via the resulting Markov models with those obtained via the corresponding simulation models. The results of this experiment show that our proposed approach obtains numeric values that are significantly more accurate than those obtained via classical queuing models.;The queuing models developed within the proposed framework can be used to compare the impact of different line-management policies, i.e., operational rules, and to answer various what-if questions regarding the cycle time of SMS toolsets. Hence these models can be employed for mid to long-range capacity planning of the toolsets as well as for assessing the factory cycle time under various conditions.