High breakdown estimator to robustify phase II control charts

Hotelling's T2 chart is one of the most popular multivariate control charts for monitoring independently and identically distributed random vectors. This chart is able to detect many types of out-of-control signals, but it is not sensitive to a small shifts in the mean vector. Classical estimation methods for multivariate control charts will not yield efficient control limits if there is instability in the data sets. The presence of outlying observations may influence standard measures such that for the points close to the center, the corresponding mahalanobis distances are improperly large and for the outliers are relatively small. Hence, the main em-phasis in this thesis is to propose a robust control chart which is less sensitive to the presence of outliers. We propose a more efficient T2 control charts based on the Re-weighted MVE (RMVE) and Re-weighted MCD (RMCD)estimators. Since the distribution of the T2 RMV E and the T2 RMCD are intractable, we propose a closed form control limits based on the estimated nonlinear regression function whereby the 1¡®% quartile of the T2 RMV E and the T2 RMCD are regressed against Our simulation studies showed that when the process is in-control, and the sample size is small, the best control chart is the standard T2, as noted in the literatures. Nonetheless, for a large sample size, the performance of the T2 RMV E and the T2 RMCD are reasonably close to the classical T2 chart. On the other hand, when there are outliers in phase I, the T2 RMV E and the T2 RMCD charts are more effective than the standard T2 and the ordinary MVE and the MCD based chart

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