On Model Selection for Autocorrelated Processes in Statistical Process Control

Using traditional control charts to monitor autocorrelated processes is not beneficial, because it will lead us to misleading detections in the processes. One of the methods used to deal with the control charts for autocorrelated process is the model-based approach. It uses an adequate time series model that fits the process and uses the residuals as monitoring statistics. For the said purpose, it is important to pick a suitable model that can adequately be used for different designs of control charts under specific time series model. This study intends to do the same for three popular types of charts namely Shewhart, exponentially weighted moving average, and cumulative sum. The models covered in this study include AR(1), MA(1), and ARMA(1,1) as the potential models to fit the process of interest. We have focused on two performance aspects namely efficiency and robustness. Average run length is used as a performance measure for different in-control and out-of-control states of the autocorrelated processes under varying levels of autocorrelation. An application example based on a real data set is also included in the study to highlight the importance of the study proposals.