Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 923463, 19 pages
http://dx.doi.org/10.1155/2011/923463
Research Article

Robust Multivariate Control Charts to Detect Small Shifts in Mean

Habshah Midi1,2 and Ashkan Shabbak2

1Faculty of Science, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia
2Laboratory of Applied and Computational Statistics, Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 14 February 2011; Accepted 16 March 2011

Academic Editor: Alexander P. Seyranian

Copyright © 2011 Habshah Midi and Ashkan Shabbak. 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.

Abstract

The classical multivariate CUSUM and EWMA charts are commonly used to detect small shifts in the mean vectors. It is now evident that those charts are easily affected by outliers which may be due to small or moderate changes in the mean vector. In this paper, we propose a robust multivariate CUSUM and Robust multivariate EWMA charts to remedy the problem of small changed in scatter outliers. Both the empirical and simulation results indicate that the proposed robust multivariate CUSUM and EWMA charts offer substantial improvement over other multivariate CUSUM and EWMA charts. This article also discussed the robustness of the proposed charts, when there is a small or moderate sustained shift in the data set.