Efficient and Highly Robust Hotelling T² Control Charts Using Reweighted Mininum Vector Variance

Hotelling T² control chart is an effective tool in statistical process control for multivariate environment. However, the performance of traditional Hotelling T² control chart using classical location and scatter estimators is usually marred by the masking and swamping effects. In order to alleviate the problem, robust estimators are recommended. The most popular and widely used robust estimator in the Hotelling T² control chart is the minimum covariance determinant (MCD). Recently, a new robust estimator known as minimum vector variance (MVV) was introduced. This estimator possesses high breakdown point, affine equivariance and is superior in terms of computational efficiency. Due to these nice properties, this study proposed to replace the classical estimators with the MVV location and scatter estimators in the construction of Hotelling T² control chart for individual observations in Phase II analysis. Nevertheless, some drawbacks such as inconsistency under normal distribution, biased for small sample size and low efficiency under high breakdown point were discovered. To improve the MVV estimators in terms of consistency and unbiasedness, the MVV scatter estimator was multiplied by consistency and correction factors respectively. To maintain the high breakdown point while having high statistical efficiency, a reweighted version of MVV estimator (RMVV) was proposed. Subsequently, the RMVV estimators were applied in the construction of Hotelling T² control chart. The new robust Hotelling T² chart produced positive impact in detecting outliers while simultaneously controlling false alarm rates. Apart from analysis of simulated data, analysis of real data also found that the new robust Hotelling T² chart was able to detect out of control observations better than the other charts investigated in this study. Based on the good performance on both simulated and real data analysis, the new robust Hotelling T² chart is a good alternative to the existing Hotelling T² charts.