Weighted Cumulative Sum Technique

Abstract

A class of weighted control schemes that generalizes the basic cumulative sum (CUSUM) technique is introduced. The schemes of the first type, in which the weights represent information concomitant with the data, prove to be especially useful when handling charts corresponding to samples of varying sizes. The schemes of the second type are based on giving greater weight to more recent information. Representatives of this class are shown to have better run length characteristics with respect to drift in the level of a controlled process than does the classical CUSUM, while maintaining good sensitivity with respect to shifts. Analogous to the classical CUSUM scheme, they admit a dual graphical representation; that is, the scheme can be applied by means of a one- or two-sided decision interval or via a V mask. A special case of this type of scheme, designated the geometric CUSUM, is considered in detail. It can be viewed as a CUSUM-type counterpart of the exponentially weighted moving average.

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