Robust Estimator Detection Outlier Points in First Phase of Multivariate Quality Control Chart with Hierarchical Clustering Technique

The main objective of performed researches in the field of multivariate statistical process control is to consider the correlation between multiple qualitative attributes for one step of process. In the second phase of the multivariate process control procedure, the rest of process is being studied whether it is under control, using the achieved control limits from the first phase and future observations. So, having found the outlier points of the first phase before the control limits to be computed, it is considered as an important issue. In order to detect these outlier points, Variety of techniques, that the majority of them rely on primary random samples, are proposed. These primary random points can effect on the precision of algorithms and final solution of the problem. In this paper, a robust estimator is issued applying hierarchical clustering technique that is not affected by outlier data in sample or unusual data, rather than the model assumptions and will detect the outlier points in multivariate control charts of the first phase in order to get them removed. Then, the proposed method is evaluated by creating the variety of scenarios from outlier points and the final outcome is compared with the Classical Hoteling and the least determinant covariance estimator. The evaluations represent that the proposed method detects more outlier points in less time rather than the former performed researches.