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Activity Number: 324 - Leading with Statistics: Process Monitoring and Improvement
Type: Invited
Date/Time: Tuesday, July 31, 2018 : 10:30 AM to 12:20 PM
Sponsor: Quality and Productivity Section
Abstract #326585 Presentation
Title: To Shrink or Not to Shrink: Hotelling's T2 Control Charts Based on Shrunken Covariance Estimates
Author(s): Allison Jones-Farmer* and Steve Rigdon and Debbie Shepherd
Companies: Miami University and St. Louis University and Louisiana State-Shreveport
Keywords: Monitoring; Process Control; SPC

Several authors have studied the effect of parameter estimation on Phase II control charts and have shown that large reference samples are necessary for the charts to perform as desired. For higher dimensional data, even larger samples are required to achieve stable estimates of the parameters. Shrinkage estimation has been widely studied as a method to achieve stable estimation of the covariance matrix. We investigate the average run length (ARL) distribution of the Phase II Hotelling's chart when using a shrunken covariance matrix. Specifically, we explore the following questions:(1) Does the use of a shrinkage estimator of the covariance matrix result in reduced variability in the ARL performance of the chart? (2) Does the use of a shrinkage estimator of the covariance matrix result in a reduced occurrence of "strictly multivariate" false alarms on the chart? (3) How does shrinkage of the covariance matrix affect the out-of-control performance of the chart? (4) How does "overshrinking" influence the ARL performance of the chart? Our results show that the benefits of shrinkage estimation are small and may not justify the use of the more advanced estimation method.

Authors who are presenting talks have a * after their name.

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