Optimal design of general linear filters for statistical process control

Statistical Process Control (SPC), and in particular control charting, is widely used to achieve and maintain control of a process and reduce variation. Conventional control charts are based on the assumption that observations are independently and identically distributed (i.i.d.) over time. With increasing automation, however, inspection rates have been increased. As a result, data are more likely to be autocorrelated, which could deteriorate control charting performance significantly. Many control chart modifications have been proposed to monitor autocorrelated processes. One approach is to monitor the original autocorrelated data using conventional control charts with modified control limits. Another common approach is to apply conventional control charts with normal control limits to the uncorrelated residuals of an appropriate Autoregressive Moving Average (ARMA) model. Many control charting methods, in particular those for autocorrelated data, can be viewed as simply charting the output of a linear filter applied to the process data. We propose a generalization of this concept for SPC purpose. The focus of this paper is on optimizing the design of the general linear filters, in terms of minimizing the out-of-control Average Run Length (ARL) while constraining the in-control ARL to some desired value. The optimal general linear filters are compared with other methods in tenus of ARL performance and a number of their interesting characteristics are discussed for various types of mean shifts (step, spike, sinusoidal) and various ARMA process models.