Two robust control charts for group-wise monitoring of the multivariate data

The goal of this paper is to detect the mean shift in the process of the multivariate data, and the decision should be made in group-wise, which means that when at least one individual within a group is out-of-control (OC), the corresponding group is OC. The research on group-wise monitoring of the univariate data is very common, while the research on group-wise monitoring of the multivariate data is very rare. The existing two control charts for group-wise monitoring of the multivariate data only perform well for the given OC scenario, and perform poorly in other OC scenarios. However, in reality, the OC scenario is often unknown in advance due to the difficulty in obtaining available prior information. Thus, this paper proposes two new types of Phase II robust control charts, which utilize the best features of the existing control charts. The two control charts are compared with the existing control charts in terms of the true positive rate, and three relative mean indices. Numerical results show that these proposed control charts are able to balance the detection of various OC scenarios, and outperform the existing control charts. Finally, the superiority and the robustness of the proposed control charts are illustrated through a real example from a semiconductor manufacturing process.