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

该项目将有助于科学的进步，并将有利于国家的繁荣和福利，通过加强制造系统的监测和质量控制。昂贵的高科技制造过程需要早期检测过程干扰和准确的产量预测。早期检测允许更快地诊断干扰的性质和原因并对其进行校正，以提高质量并降低生产成本。该项目将为表现出空间和/或时间依赖性的各种应用设计和测试新的预测方法。 通过利用这些依赖性，该项目有望提高质量并降低制造成本。 该项目还与表现出空间和时空依赖性的其他领域相关，例如通过检测垃圾邮件等不良链接行为模式来控制传染病的传播和加强对社交网络上个人的保护。这项工作的基本概念和预测方法的新观点将被纳入教育课程材料。本科生和研究生都将参与制造业和医疗保健领域的研究和实施。本项目利用图论优化技术将时空依赖性明确纳入预测和估计问题。 图论方法采用分离偏差模型，其目标是最小化涉及与节点相关联的偏差函数和与边缘相关联的分离函数的惩罚函数。 有效的参数切割算法凸偏差和双线性分离将得到扩展和改进。 将研究基于实际晶圆缺陷数据的先验信息的集成电路制造良率预测的分离函数。 这项工作将为贝叶斯估计、机器学习和保序回归中广泛使用的基本分离偏差模型的扩展模型和计算算法的理论发展做出根本性贡献。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估而被认为值得支持。

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.