A Study on the Multivariate Combined Control Chart

In this research, we propose multivariate combined control charts for the mean vector and covariance matrix to control simultaneously in the process under the normality assumption. For doing this, first of all, we review the multivariate simultaneous tests proposed by Park (2018) in some detailed fashion, which makes use of the likelihood ratio principle. Also we consider the simultaneous tests with various combining functions to combine individual tests. Then we propose to construct the multivariate combined charts by investigating the relation between the hypothesis test and control chart to utilize the multivariate simultaneous tests. We note that the proposed control charts will be consisted with a series of hypothesis tests instead of plotting the values of sample mean vector and covariance matrix in the control chart sheets. Then we investigate the efficiency among the proposed control charts by obtaining empirical average run length which represents the average runs until detecting out of control state when the process is out of control. Finally, we observe some interesting features related with the multivariate combined control charts.