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Statistical Process Monitoring with Integrated Moving Average Noise¹

S. A. Vander Wiel AT & TBell Laboratories Murray Hill, New Jersey

Abstract

One of the most inappropriate assumptions in traditional control charting technology is that process data constitutes a random sample. In reality most process data is time-ordered and autocorrelated. This paper shows that a sensible approach to monitoring such data depends upon the specific details and goals of each particular application. Sometimes traditional control charts with wider-than-usual action limits are sufficient. Other times a morę refined approach is necessary.

One refined approach is to monitor forecast errors from a time series model of the process. We show that a sudden level shift in an integrated moving average process results in a pattemed shift in the mean of forecast errors. Initially the mean shifts by the same amount as the process level but then it decays geometrically back to zero. Of the many altemative monitoring schemes for this kind of data, we study four: cumulative sums (CUSUMs),

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A portion of this chapter is based on “Monitoring Processes that Wander Using Integrated Moving Average Models,” by Scott A. Yander Wiel Technometrics, May 1996, vol. 38.