DESIGNING A HOTELLING T2 CONTROL CHART USING CLUSTERING

The main purpose of the researches in the field of multivariate statistical process control is to consider the correlation between several qualitative characteristics for a specific stage of the process. In Phase II, the multivariate process control procedure is investigated using the control limits obtained from Phase I and online observations of the process are controlled. Finding the outliers of the first phase before calculating the control limits to achieve a suitable result is of great importance. Therefore, in this research, the proposed control diagram identifies outliers using hierarchical clustering method. The importance of this method is in determining the outliers using heterogeneity coefficient and a set of variable control limits. In this method, the heterogeneity coefficient and a set of control limits are determined using the parameters of sample size and number of variables (qualitative indicators). In fact, the distance between observations is modeled in clusters while the outliers are deleted by the recursive algorithm. Then, the mean and matrix of variance and covariance T2 are determined based on the remaining data. In the last step, according to the obtained control limit, T2 statistic is determined. To evaluate the performance of the proposed control chart and compare it with the classic T2 hoteling chart in identifying outliers, the noncentrally index and the method of Alfaro et al. have been used based on the detection of outliers data. Two diagrams from the Hawkins and Phosphorus datasets have also been examined for further comparison. The importance and efficiency of the proposed method were observed despite a large number of outliers in the data set.