Adding a "Slope" Calibration Mask to your CUSUM chart

For the aid of the viewers of your CUSUM (or your own reference) it is useful to add a calibration scale to the CUSUM. Remember that with a CUSUM its the slope of the trend that conveys the average, and changes in slope that indicate increases or decreases in the underlying data.

The simplest way to add the scale is to add a few series (typically 3) representing reference values for a short period at the beginning of the graph. It might look something like this picture.


To generate values for the series, simple use the same CUSUM method on the calibration value, using the same mean that used previous to generate the CUSUM.

For example, the CUSUM slope for the value 5 might start like this in column G:

[Cell G4] = G3+5-$B$3
[Cell G5] = G4+5-$B$3
where $B$3 is the mean you calculated previously.

Here's the example spreadsheet.

Happy charting!

Interpreting CUSUM graphs

To interpret the CUSUM graph one needs to look at the slope of the graph, and specifically where slope changes occur. A constant slope is an indication of a stable value in the underlying data despite the presence of noise. In the example given earlier, a number of relatively "constant" slope areas can be identified, and these are shown superimposed on the graph. Points at which the slope changes are the turning points and these have been denoted with vertical lines.

So what do you do with the turning points? We'll this gives you an indication of where to average values from. In the example given, the first identified period is from t=1..14s, and the average for this period is 1.0. For the second period t=15..30s, the average is 6.4, and so on. I haven't shown this but you you could add this graphically to the bottom series as straight lines between the turning points for clarity, at the appropriate y-axis average value.

There is some danger in identifying too many turning points, as you could start reading something into the data which just isn't there. The greater the change in slope, the more convincing the turning point. In this example the turning points near 48, 72 and 84 are the most convincing.

To assist in calculating the average from the graph, one can add a calibration scale/mask which shows the relationship between set slopes and average values. We'll save details on how to do that for a later post though.