High Breakdown Estimation Methods for Phase I Multivariate Control Charts

• Activity Number: 234
• Type: Contributed
• Date/Time: Tuesday, August 9, 2005 : 8:30 AM to 10:20 AM
• Sponsor: Section on Quality and Productivity
• Author(s): Willis Jensen*+ and Jeffrey B. Birch and William H. Woodall
• Companies: Virginia Polytechnic Institute and State University and Virginia Polytechnic Institute and State University and Virginia Polytechnic Institute and State University
• Keywords: Minimum covariance determinant ; Minimum volume ellipsoid ; Multivariate SPC ; Outliers ; Breakdown point ; Profile monitoring

Abstract

The goal of Phase I monitoring of multivariate data is to identify multivariate outliers and other anomalies so the estimated control limits are sufficiently accurate for Phase II monitoring. Control limits estimated by classical methods are not capable of detecting outliers, but Vargas (2003) showed a high breakdown estimation method based on the minimum volume ellipsoid (MVE) is well suited to detecting multivariate outliers in data for certain sample sizes and levels of contamination. However, estimators based on the MVE can be difficult to implement in practice due to the extensive computation required to obtain the estimates. In contrast, estimators based on the minimum covariance determinant (MCD) are well suited in detecting multivariate outliers but are easier to implement and have better asymptotic properties. For many sample sizes and levels of contamination, they have equal or superior performance to the MVE in terms of the probability of a signal. Guidance is for when to use which estimator. High breakdown estimation methods can be applied to a variety of multivariate quality-control data.