Some selective process models
As we mentioned in the introduction, there are two approaches used to handle the problem of monitoring the autocorrelated processes. In this study, we consider the model-based approach, it starts by fitting an adequate time-series model on the process, then obtain the residuals of the model to eliminate its autocorrelation, at the end, use these residuals as a monitoring statistic.
The adequate model is picked by Box–Jenkins method, then it is diagnosed by characteristic shape of the autocorrelation function (ACF) and partial ACF (PACF), which are necessary tools to identify the adequateness of the time series model; for more details, see Reynolds18 and Box and Jenkins.