The conventional cumulative sum (CUSUM) with k = 0.5 is often used as the default CUSUM statistic when future shifts are unknown. In this paper, CUSUM procedures are designed to be efficient at signalling a range of future expected but unknown location shifts. Two approaches are advocated. The first uses three simultaneous conventional CUSUM statistics with different resetting boundaries. This results in a procedure that has, on average, several levels of memory, and thus signals a broader range of location shifts more efficiently than the conventional CUSUM with k = 0.5. The second uses an adaptive CUSUM statistic that continually adjusts its form to be efficient for signalling a one-step-ahead forecast in deviation from its target value. Average run length (ARL) is used to compare the relative performance of procedures. Several applications are used to illustrate procedures.
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