Improved Multivariate Control Charts with Robust Methods - Shabbak, Ashkan (2011)
In real life, usually more than one important quality characteristic of a products and services are considered. In this situation, a multivariate control chart is appropriate to simultaneously monitor more than one quality characteristics. Three of the most popular multivariate statistical quality control charts are Hotelling’s T2, the MCUSUM (Multivariate Cumulative Sum) and MEWMA (Multivariate Exponentially Weighted Moving Average). Unfortunately, it is now evident that all these classical charts are easily affected by multiple outliers which may appear as a scatter outliers or sustained shift in the drawn dataset. To remedy this drawback, only recently robust methods such as the Minimum Volume Ellipsoid (MVE) or the Minimum Covariance Determinant (MCD), be applied to multivariate control process applications. In this thesis, the performance of robust control charts, based on the MVE and MCD, for individual observations is extensively studied when there is a sustained shift in the dataset. The results of the study reveal that the robust control charts is more efficient in detecting the sustained shift than the classical charts. The existing study on robust control charts are mainly focussed on individual observation. However, in real situation, we often encountered more than one observation in each variable of each subgroup. Hence, in this situation, we propose a robust control charts based on the MVE and MCD estimators, in the case of scatter outliers. Our findings show that both the proposed robust control charts outperform the classical chart, in the situation of more than one observation in each variable of each subgroup in the presence of scatter outliers. We also propose applying the robust median and MAD (Med-Mad) cut-off points as control limits to the MVE-based and the MCD –based control charts. The performance of this new proposed empirical control limits are investigated when a sustained shift exists in the mean vector. The real examples and simulation studies signify that the proposed control limits are better than the existing control limits for detecting the sustained shift in a dataset.