Joint Multivariate Control Charts with Both the First Few and the Remaining Principal Components

• Activity Number: 412
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Korean International Statistical Society
• Author(s): Sungim Lee*+ and Johan Lim
• Companies: Dankook University and Seoul National University
• Keywords: Multivariate control chart ; Principal components ; Q-statistic ; Spiked covariance model ; Average run length

Abstract

Due to recent advance of computer technology, we are often required to monitor and control the process of high-demensional multivariate characteristics of interest. To do this, one popular method is the (multivariate) control chart based on the Hotelling's T-squared statistic. In building the Hotelling's T-squared statistic, it is common to use a few largest principal components to have a better visualization of the process as well as to resolve possible difficulties from the high-dimensionality. However, the use of the first few principal components is limitted to detect the abnormality in the retained direction, and, undoubtly, fails to tell the changes in other directions. To this reason, in this paper, we propose to control the largest and the remaining principal components jointly particularly in the spiked covariance model. We study some statistical properties of the proposed procedure, and numerically compare its performance with existing multivariate control charts.