Multivariate Control Charts Based on Trimmed Means

Article

Alloway, James A.; Raghavachari, M.   (1990, ASQC)   Syracuse University, Oak Brook, IL; Rensselaer Polytechnic Institute, Troy, NY

Annual Quality Congress, San Francisco, CA    Vol. 44    No. 0
QICID: 9491    May 1990    pp. 449-453
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Article Abstract

Langenberg and Iglewicz [9], White and Schroeder [13] and Iglewicz and Hoaglin [6] present approaches to trimmed mean control charts for the univariate case. They show that these control charts offer advantages if the underlying distribution is not normal, or if the distribution arises out of gross error models. Alloway and Raghavachari [2] compare the trimmed mean control charts with the control charm developed by them using the Hodges-Lehmann estimator and point out the good performance of the charts based on the trimmed mean.

This paper presents an alternative method of constructing control charts based on the trimmed mean for the univariate case as well as control charts for the multivariate case for the first time in the literature. For the univariate case, the method is based on the concept of the trimmed t- statistic developed by Tukey and McLaughlin [12]. The proposed method is compared with that of Langenberg and Iglewicz for a large class of distributions through simulation.

The univariate control charts are generalized to the multivadate case. The assumption of non-normality is even more realistic in the multivariate context and the control charts based on robust statistics such as trimmed means would be more appropriate in this situation. The trimmed t- statistic is generalized in much the same way that Hotelling [5] did for the univariate t- statistic. A numerical example of the bivariate case using the telephone pole data from Shewhart [10] is presented and comparisons are made with the control charts based on Hotelling's T 2.

Keywords

Statistics,Control charts,Normality


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