A Distribution-Free Multivariate Phase I Location Control Chart for Subgrouped Data from Elliptical Distributions

Abstract

In quality control, a proper Phase I analysis is essential to the success of Phase II monitoring. A literature review reveals no distribution-free Phase I multivariate techniques in existence. This research develops a Phase I location control chart for multivariate elliptical processes. The resulting in-control reference sample can then be used to estimate the parameters for Phase II monitoring. Using Monte Carlo simulation, the proposed method is compared with the Hotelling's T² Phase I chart. Although Hotelling's T² chart is preferred when the data are multivariate normal, the proposed method is shown to perform significantly better under nonnormality. This article has supplementary material online.

KEY WORDS:

• Data depth
• Mahalanobis depth
• Mean rank chart
• Nonparametric
• Outliers
• Retrospective analysis
• Robust estimators

ACKNOWLEDGMENTS

The authors thank the Editor, Associate Editor, and anonymous referees for their guidance and helpful suggestions that greatly improved the presentation of this research. We also thank Sidi Niu, Northeastern University, for allowing us to use his MATLAB code to evaluate sample elliptical symmetry and to include this code as supplemental material for the readers. The authors are extremely grateful to Dr. Robert Serfling, Dr. Joe Sullivan, and Dr. Styaki Mazumder for their assistance and keen insights.