Robust Maximum Half-Normal Multivariate Control Chart

Every company conducts evaluations to ensure the quality of its product and services. One useful tool is the control chart. Multivariate simultaneous control charts, such as Max-Mchart, Max-Half-Mchart, Max-MEWMA, and Max-MCUSUM, are used to monitor the mean and variability simultaneously. The Max-Half-Mchart is advantageous because it can detect both small and large shifts in the mean and covariance matrix. However, outliers can cause the chi-square cumulative distribution function to approach one, leading the inverse standard normal cumulative distribution toward infinity and triggering masking and swamping effects. To overcome this, robust estimators of the mean and covariance matrix are required. Fast-MCD and Det-MCD are fast robust estimators based on the C-step algorithm. The results of the outlier detection show that the robust Max-Half-Mchart based on Det-MCD performs best for a small number of outliers, while the robust Max-Half-Mchart based on Fast-MCD and Det-MCD performs best for a large number of outliers. In terms of process shift detection, both robust Max-Half-Mchart based on Fast-MCD and Det-MCD can detect shifts effectively. Applications to OPC cement quality data and synthetic data indicate that the robust Max-Half-Mchart based on Det-MCD is the most sensitive to outliers.