Some properties of the EWMA control chart in the presence of autocorrelation

Schmid extended the classical EWMA control chart to autocorrelated processes. Here, we consider the tail probability of the run length in the in-control state. The in-control process is assumed to be a stationary Gaussian process. It is proved that the tails for the autocorrelated process are larger than in the case of independent variables if all autocovariances are greater than or equal to zero. The inequality is strict. Moreover, this result is still valid for stationary processes having elliptically contoured marginal distributions.