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Thresholded Multivariate Principal Component Analysis for Phase I Multichannel Profile Monitoring

Summary: Monitoring multichannel profiles has important applications in manufacturing systems improvement, but it is nontrivial to develop efficient statistical methods because profiles are high-dimensional functional data with intrinsic inner- and interchannel correlations, and that the change might only affect a few unknown features of multichannel profiles. To tackle these challenges, we propose a novel thresholded multivariate principal component analysis (PCA) method for multichannel profile monitoring. Our proposed method consists of two steps of dimension reduction: It first applies the functional PCA to extract a reasonably large number of features under the in-control state, and then uses the soft-thresholding techniques to further select significant features capturing profile information under the out-of-control state. The choice of tuning parameter for soft-thresholding is provided based on asymptotic analysis, and extensive numerical studies are conducted to illustrate the efficacy of our proposed thresholded PCA methodology.

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  • Topics: Statistics
  • Keywords: Change-point, Multichannel profiles, Principal component analysis, Shrinkage estimation, Statistical process control
  • Author: Wang, Yuan; Mei, Yajun; Paynabar, Kamran
  • Journal: Technometrics