CUSUM: Cumulative Summary

The CUSUM plot is used widely in Marketing and Financial analysis to track cumulative changes in a time-ordered quantity. The way I calculate a CUSUM for the plots you see on my blood pressure page is:
  1. Subtract the mean (or median) of the data off of each data point's value.
  2. For each point, Add all the mean/median-subtracted points before it.
  3. The resulting values are the Cumulative Summary (CUSUM) for each point.
In manufacturing, the mean/median is not used but rather a "target" value that represents what you would like to reach in the long-term (for example, some measure of quality or performance). They also set "alarms" which are values that the CUSUM should not go above or below.

The CUSUM test is useful in picking out general trends from random noise as noise will tend to cancel out in the long-run (there are just as many positive and negative values of true noise) but a trend will show up as a gradual departure from zero in the CUSUM. For my plots, I do the CUSUM on my raw data and I use the mean value of the raw data as the target.

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