Introduction of a Robust Hotelling T2 Control Chart

One of the most widely used multivariate control charts isthe Hotelling T2. In order to design a Hotelling T2 controlchart, the mean vector (μ) and the variance-covariancematrix (Σ) must be first estimated. The classical estimatorsare usually used to estimate these two parameters. They aredefined based on assumptions which are not always valid.One weakness of the classical estimators is their sensitivityto the presence of outliers. One way to deal with outliers isto use robust estimators. In this study, a robust Hotelling T2control chart is proposed. The mean vector for the controlchart is obtained using the sample median. The medianabsolute deviation from the sample median and thecomedian estimators are used to calculate the elements ofthe variance-covariance matrix. The proposed robustestimators of the mean vector and the variance-covariancematrix are compared with the sample mean vector and thesample variance-covariance matrix through efficiency androbustness measures. The performances of the proposedrobust Hotelling T2 control chart and the classical one arealso compared by means of ARL. The simulation resultsreveal that, the proposed robust Hotelling T2 control charthas a much better performance than the classical HotellingT2.

Keywords:

Robust estimators , local contamination , global contamination , median , MAD and COM estimator