ASQ - Statistics Division

Autocorrelated Data and SPC – Mini Paper Taken from the Summer 1993 Newsletter

Abstract: A primary purpose of control charts is to track important process or quality characteristics over time to detect departures from “statistical control”. Traditionally, the definition of statistical control has included only the case of independent and identically distributed (i.i.d.) observations. Many processes, however, exhibit some degree of time dependent autocorrelation. Autocorrelation has an effect on the statistical performance of control charts. Positive autocorrelation results in more signals for control charts. However autocorrelation is a characteristic of the process as a whole and not necessarily an indicator of special cause. Thus, if autocorrelation is present, but unrecognized, then one can misinterpret control charts. Given that autocorrelation is present, one proper course of action is to first try to remove the effect of autocorrelation. If the autocorrelation cannot be removed it might be possible to model the autocorrelation and use a feedback control scheme to reduce variability around a specified target value. If these are not viable solutions, some recommend fitting a time series model to the autocorrelated data and then monitoring the one-step-ahead forecasts, i.e. residuals. Finally, one more option for dealing with autocorrelation, when its source cannot be removed and feedback control is not possible, is to sample less often. Each method has corresponding advantages and disadvantages.

Keywords: Autocorrelation - Control charts - Shewhart chart - X bar - CUSUM chart - Exponentially weighted moving average (EWMA) chart - Residuals

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