Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 531864, 15 pages
Research Article

An Improvement of the Hotelling 𝑇 𝟐 Statistic in Monitoring Multivariate Quality Characteristics

1Statistical Research and Training Center (SRTC), 1433873487 Tehran, Iran
2Laboratory of Computational Statistics and Operation Research, Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Malaysia
3Mathematics Department, Faculty of Science, University Putra Malaysia, 43400 Serdang, Malaysia

Received 4 November 2011; Revised 3 February 2012; Accepted 3 February 2012

Academic Editor: Hung Nguyen-Xuan

Copyright © 2012 Ashkan Shabbak and Habshah Midi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Hotelling 𝑇 2 statistic is the most popular statistic used in multivariate control charts to monitor multiple qualities. However, this statistic is easily affected by the existence of more than one outlier in the data set. To rectify this problem, robust control charts, which are based on the minimum volume ellipsoid and the minimum covariance determinant, have been proposed. Most researchers assess the performance of multivariate control charts based on the number of signals without paying much attention to whether those signals are really outliers. With due respect, we propose to evaluate control charts not only based on the number of detected outliers but also with respect to their correct positions. In this paper, an Upper Control Limit based on the median and the median absolute deviation is also proposed. The results of this study signify that the proposed Upper Control Limit improves the detection of correct outliers but that it suffers from a swamping effect when the positions of outliers are not taken into consideration. Finally, a robust control chart based on the diagnostic robust generalised potential procedure is introduced to remedy this drawback.