Equilibria, Stability, Oscillations, Chaos, and Transients in Re-entrant Lines

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This research project is devoted to performance analysis and improvement of production systems widely used in semiconductor manufacturing - the re-entrant lines. It is universally accepted that performance of re-entrant lines is characterized by large variability and oscillations of the throughput (TP) and work-in-process (WIP). This leads to performance degradation and long and unpredictable production cycle time. At present, no rigorous explanations of these phenomena are available, and the attempts to combat them are far from being successful. The research is intended to develop a theory that explains fundamental reasons for these phenomena and provide techniques for their alleviation. The approach is based on the methods of nonlinear dynamics. Specifically, the project will investigate steady states of re-entrant lines, their (Lyapunov) stability properties, periodic and chaotic oscillations, and transient behavior (i.e., the processes of convergence to steady states after machine breakdowns). As a result, the project will provide analytical tools for investigating the performance of re-entrant lines, including TP and WIP variability, and offer quantitative methods and qualitative insights that can be used by production personnel to mitigate the undesirable dynamic phenomena.The broader impact of this research will be attained through industrial short courses to be offered by the PI at semiconductor manufacturing plants. These courses will present the results of this research in the format appropriate for factory floor applications. The PI has been offering similar courses in the automotive industry for over ten years, where the results of prior NSF-supported research on serial lines and assembly systems have been presented. As an outcome, some of these results have been incorporated in standard operating procedures at several automotive plants and led to a substantial performance improvement. Similar outcomes are expected to be obtained in the semiconductor industry as well.