A Graph Theoretic Approach for Spatial Dependence in Quality Control and Prediction

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This project will contribute to the advancement of science and will benefit the national prosperity and welfare, by enhancing manufacturing system monitoring and quality control. Expensive high-tech manufacturing processes require early detection of process disturbances and accurate yield prediction. Early detection allows for faster diagnosis of the nature and cause of the disturbances and their correction in order to improve quality and reduce production costs. This project will devise and test new prediction methods for diverse applications that exhibit spatial and/or temporal dependencies. By exploiting these dependencies, this project is expected to enhance quality and reduce production costs in manufacturing. The project also has relevance to other domains that exhibit spatial and spatio-temporal dependencies, such as control of the spread of communicable disease and enhanced protection of individuals on social networks by detecting patterns of adverse link behavior, such as spam. The fundamental concepts of this work and the new outlooks on prediction approaches will be incorporated into educational course materials. Both undergraduate and graduate students will be involved in the research and implementation in the areas of manufacturing and health care.This project utilizes graph theoretic optimization techniques to explicitly incorporate spatiio-temporal dependencies in problems of prediction and estimation. The graph-theoretic approach employs a separation-deviation model where the objective is to minimize a penalty function involving deviation functions associated with nodes and separation functions associated with edges. Efficient parametric cut algorithms for convex deviation and bilinear separation will be extended and improved. Separation functions for integrated circuit manufacturing yield prediction based on priors from actual wafer defect data will be examined. This work will make fundamental contributions to the theoretical development of models and computational algorithms for extensions of the basic separation-deviation model, which is used extensively in Bayesian estimation, machine learning, and isotonic regression.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.