Contributions to fault detection and diagnosis with high-dimensional data
- Motivated by applications to root-cause identification of faults in multistage manufacturing processes which involve a large number of tools or equipments 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. The problem of detection and diagnosis of abrupt changes in a stochastic system on the basis of sequential observations has many applications, some of which are discussed in this thesis. In statistical process control (SPC), the past decade witnessed the emergence of a new direction in quality control because of the availability of big data, making use of contemporaneous developments in the statistics literature on high-dimensional data analysis. It has been noticed that in multivariate and high-dimensional applications, only a sparse subset of quality characteristics or other variables of interest undergoes abnormal changes that lead to deviations from the state of statistical control. The past decade also witnessed major developments in surveillance over sensor networks, cyber-security and information systems. We give a general theory for sequential fault detection in these stochastic models and also modify and extend it to the much less developed problem of fault diagnosis. This fault diagnosis, or change isolation problem, is to determine upon detection of change in a system which one in a set of possible changes has actually occurred. In this connection, we also develop a parallel theory of sequential multiple hypothesis testing.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Stanford University, Department of Statistics.
|Lai, T. L
|Lai, T. L
|Statement of responsibility
|Submitted to the Department of Statistics.
|Thesis (Ph.D.)--Stanford University, 2015.
- © 2015 by Milan Shen
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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