Combined Control Charts for the Mean and Variance using Likelihood Method

In this study, we consider to propose combined control charts for the process mean and variance to control simultaneously assuming that the process distribution is normal. For this, first of all, we review the existing combined control charts and then propose a new chart based on the union-intersection test with the jointly likelihood ratio statistics for the mean and variance. Then we apply the Liptak combining function to propose another combined control chart. For the construction of those combined control charts, we use the fact that a series of the hypothesis tests is equivalent to the maintenance of a control chart. In order to combine the two individual tests for the respective mean and variance, we utilize the p-values for both individual tests since the two likelihood ratio statistics have different forms. Then we compare the performance of the combined charts reviewed and proposed in this study by obtaining the empirical probabilities detecting the out-of-control state when the process becomes out-of-control under the five different scenarios through a simulation study. Finally, we discuss some interesting aspects which are related with the combined charts as concluding remarks.