Design of exponentially weighted moving average control charts for autocorrelated processes with model uncertainty

Residual-based control charts are popular methods for statistical process control of autocorrelated processes. To implement these methods, a time series model of the process is required. The model must be estimated from data, in practice, and model estimation errors can cause the actual in-control average run length to differ substantially from the desired value. This article develops a method for designing residual-based exponentially weighted moving average (EWMA) charts under consideration of the uncertainty in the estimated model parameters. The resulting EWMA control limits are widened by an amount that depends on a number of factors, including the level of model uncertainty.