A Note on the Combined Control Charts based on the Simultaneous Tests

In this study, first of all, we review several simultaneous tests for the mean and variance under the normality assumption. With formulating the null hypothesis and its alternative, we consider applying the joint test statistics which have been derived using the likelihood ratio principle and combination functions to combine the individual partial tests for the simultaneous tests. We use the individual p-values for each partial test to construct the simultaneous tests and obtain the overall p-values to complete the simultaneous tests using the null distributions for the combination functions. Then we apply these simultaneous tests to the statistical process control with discussion for running the combined charts for an industrial example based on the idea that a series of hypothesis test and maintenance of control chart are equivalent. Finally we discuss some interesting features about the simultaneous tests and combined charts with simultaneous confidence region as concluding remarks.