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Alternative Hotelling's T 2 Charts using Winsorized Modified One‐Step M‐estimator
Author(s) -
Haddad F. S.,
SyedYahaya S. S.,
Alfaro J. L.
Publication year - 2013
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.1407
Subject(s) - estimator , covariance matrix , outlier , control chart , chart , statistics , mathematics , trimming , constant false alarm rate , computer science , algorithm , process (computing) , operating system
Hotelling's T 2 chart is a popular tool for monitoring statistical process control. However, this chart is sensitive in the presence of outliers. To alleviate the problem, this paper proposed alternative Hotelling's T 2 charts for individual observations using robust location and scale matrix instead of the usual mean vector and the covariance matrix, respectively. The usual mean vector in the Hotelling T 2 chart is replaced by the winsorized modified one‐step M‐estimator ( MOM ) whereas the usual covariance matrix is replaced by the winsorized covariance matrix. MOM empirically trims the data based on the shape of the data distribution. This study also investigated on the different trimming criteria used in MOM . Two robust scale estimators with highest breakdown point, namely S n and T n were selected to suit the criteria. The upper control limits for the proposed robust charts were calculated based on simulated data. The performance of each control chart is based on the false alarm and the probability of outlier's detection. In general, the performance of an alternative robust Hotelling's T 2 charts is better than the performance of the traditional Hotelling's T 2 chart. Copyright © 2012 John Wiley & Sons, Ltd.