Online Cusum Chart with YOUR Data! The CUSUM Calculator Chart

Copy a single column of numbers (max 90 rows) from Excel and paste in the form below. (Numbers should be separated by a tab- simple copy and paste should work without doing anything fancy.) Click Submit. Then after about 5 minutes refresh this page and hopefully your data as well as the CUSUM should be visible in the chart below.
*(If it doesn't happen in 10 minutes, then there is something wrong; my apologies if this is the case. It could be the format of your data or something going wrong with my code.) But hopefully it will work!


This is the output result:

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.

Applying the CUSUM to your spreadsheet data

The CUSUM is, simply put the cumulative sum of the differences of your data from its mean value.

i.e. CUSUM(t) = CUSUM(t-1) + data(t)-(mean value)

in spreadsheet for if your data is in range from A2..A32, the cusum could be implemented as follows in cells B2..B32: (Make sure cell B1 is empty equal to zero (0).)

B2=B1+A2-average($a$2..$a$32)

Then copy down to cells B3..B32.

Alternatively you could work out the average in a seperate cell and then absolute reference it.

eg. A1=average($a$2..$a$32)

then B2 would simplify to:

B2=B1+A2-$A$1

In the next post we'll cover the interpretation of the CUSUM.

In the graph shown an example of some noisy data (bottom series) and its corresponding CUSUM is presented. Click here to see the data spreadsheet.

Introducing the CUSUM chart

The Cumulative Sum chart (CUSUM) is a very useful (and powerful) tool to pick up small changes in trends of noisy data- and it works just as well if there are large trend changes. Despite what some might say, it is actually relatively easy to apply this technique in a spreadsheet to analyse your data, although one must understand how to interpret the graph.

The CUSUM is very useful to identify important dates or times (turning points) where a trend change occurred, especially where one finds that this is not obvious when looking at the time series data.
You can use it to guage the likelihood that other noisy variables could be causes if one can pick up similar trend changes in these variables. It finds applications in data analysis especially of process data and is a tool that can be used by Six Sigma practitioners.

In my next post I will elaborate on how to implement this useful technique in a spreadsheet such as Excel or OpenOffice, and also show an example, and more importantly how to interpret the graph, so stay tuned. For now, here are some related links.

Cusum Link 1 (NIST)
Cusum Link 2 (iSixSigma)