3. Performance evaluations
To investigate the performance of the control chart design under the different fitted time series models. Firstly, consider the modelbased approach to extract the residuals from a fi tted time-series model and construct the control limits according to the definitions in Section 2. Secondly, use the pseudocode in Table IV. to calculate the ARLs of the different control charts designs under the three selected time series models and introduce some values of shifts in the process mean.