Multiple Testing in Regression Models With Applications to Fault Diagnosis in the Big Data Era

Ching-Kang Inga, Tze Leung Laib, Milan Shenb*, KaWai Tsangb & Shu-Hui Yuca Institute of Statistical Science, Academia Sinica, Taipei, Taiwanb Department of Statistics, Stanford University, Stanford, Californiac Institute of Statistics, National Kaohsiung University, Kaohsiung, TaiwanCONTACT Milan Shen milanshen@gmail.com Department of Statistics, Stanford University, Stanford, CA 94305, USAColor versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/TECH.Supplementary materials for this article are available online. Please go to http://www.tandfonline.com/r/TECH.ABSTRACTMotivated by applications to root-cause identification of faults in multistage manufacturing processes that involve a large number of tools or equipment at each stage, we consider multiple testing in regression models whose outputs represent the quality characteristics of a multistage manufacturing process. Because of the large number of input variables that correspond to the tools or equipments used, this falls in the framework of regression modeling in the modern era of big data. On the other hand, with quick fault detection and diagnosis followed by tool rectification, sparsity can be assumed in the regression model. We introduce a new approach to address the multiple testing problem and demonstrate its advantages over existing methods. We also illustrate its performance in an application to semiconductor wafer fabrication that motivated this development. Supplementary materials for this article are available online.