Improved design of robust exponentially weighted moving average control charts for autocorrelated processes

Residual-based control charts for autocorrelated processes are known to be sensitive to time series modeling errors, which can seriously inflate the false alarm rate. This paper presents a design approach for a residual-based exponentially weighted moving average (EWMA) chart that mitigates this problem by modifying the control limits based on the level of model uncertainty. Using a Bayesian analysis, we derive the approximate expected variance of the EWMA statistic, where the expectation is with respect to the posterior distribution of the unknown model parameters. The result is a relatively clean expression for the expected variance as a function of the estimated parameters and their covariance matrix. We use control limits proportional to the square root of the expected variance. We compare our approach to two other approaches for designing robust residual-based EWMA charts and argue that our approach generally results in a more appropriate widening of the control limits.