An optimal filter design approach to statistical process control

Many control charts can be viewed as charting the output of a linear filter applied to process data, with an alarm sounded when the filter output falls outside a set of control limits. We generalize this concept by considering a linear filter in its most general time-invariant form. We provide a strategy for optimizing the filter coefficients in order to minimize the out-of-control ARL, while constraining the in-control ARL to some desired value. The optimal linear filters exhibit a number of interesting characteristics, in particular when the process data are autocorrelated. In many situations, they also substantially outperform an optimally designed exponentially weighted moving average (EWMA) control chart.