Thresholded Multivariate Principal Component Analysis for Phase I Multichannel Profile Monitoring

ABSTRACT

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.

KEYWORDS:

• Change-point
• Multichannel profiles
• Principal component analysis
• Shrinkage estimation
• Statistical process control

Acknowledgments

The authors thank the editor, associate editor, and two anonymous reviewers for their detailed and constructive comments that greatly improved the presentation of the article. This is part of Y. Wang's Ph.D. dissertation. The authors also gratefully acknowledge the support of the National Science Foundation under grant NSF CMMI-1362876 and CMMI-1451088.

Additional information

Funding

Division of Civil, Mechanical and Manufacturing Innovation: [1362876,1451088]; Division of Mathematical Sciences: [0954704].