The Detection Method of Small Shifts Based on Stationary Autocorrelated Process

When control charts are used to monitor a process, a standard assumption is that observations from the process at different times are independent random variables. However, the independence assumption is often not reasonable for processes of interest in many applications because the dynamics of the process product autocorrelation in the process observations. The presence of significant autocorrelation in the process observations can have a large impact on traditional control charts developed under the independence assumption. A method of monitoring little shifts in stationary autocorrelated process is discussed in this paper. At first, auto-regressive moving-average model is used to fit stationary autocorrelated process. Then, process autocorrelation can be removed by residual method, and exponentially weighted moving average charts are constructed to monitor little shifts of process mean and variance. Comparing with other methods, we can illustration that this EWMA residuals charts have better efficiency for stationary autocorrelated processes.