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

ABSTRACT

Motivated 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.

Keywords:

• Backward elimination
• Family-wise error rate
• Fault detection and diagnosis
• Lasso
• Multistage manufacturing process
• Orthogonal greedy algorithm
• Sparsity
• Wafer fabrication

Supplementary Materials

• Matlab code: Matlab code for implementing OGA_new and OGA_TS, and codes to run simulations. (GNU zipped tar file)

• Dataset: Datasets used in Section 4 of wafer QA test. (.txt file)

Acknowledgments

Ing’s research was supported in part by Academia Sinica Investigator Award. Lai’s research was supported by the National Science Foundation grant DMS-1407828. Hsu’s and Yu’s research was supported in part by the Ministry of Science and Technology of Taiwan under grants MOST 103-2118-M-390-004-MY2 and MOST 102-2118-M-390-003, respectively.