EWMA control chart limits for first- and second-order autoregressive progresses

Today’s manufacturing environment has changed since the time when control chart methods were originally introduced. Sequentially observed data are much more common. Serial correlation can seriously affect the performance of the traditional control charts. In this article we derive explicit easy-to-use expressions of the variance of an EWMA statistic when the process observations are autoregressive of order 1 or 2. These variances can be used to modify the control limits of the corresponding EWMA control charts. The resulting control charts have the advantage that the data are plotted on the original scale making the charts easier to interpret for practitioners than charts based on residuals.