As we implement the statistical process control(SPC), SPC requires statistical methodologies which detect changes in the data. A changepoint analysis has been recognized as a phase I analysis and effective for designing the control chart. The test statistics used for determining the presence of change in the data are the likelihood ratio test statistics.
We review the statistical method to find the cut-off value to be used in the test and provide the cut-off values in accordance with the probability of type I error. Since it is calculated by the quadratic approximation, it is very accurate and effective to set up the control limits for the preliminary control chart.