## 7.04.2011

### Statistical quality control tool, CUSUM Chart

In statistical quality control, the CUSUM (or cumulative sum control chart) is a sequential analysis technique.  It is typically used for monitoring change detection.

As its name implies, CUSUM involves the calculation of a cumulative sum (which is what makes it "sequential").

The advantage of CUSUM is that each plotted point includes several observations, so you can use the central limit theorem to say that the average of the points (or the moving average in this case) is normally distributed and the control limits are clearly defined. As with other control charts, CUSUM charts are used to monitor processes over time.

It is design for your personal use and it plots "success" and "failure" against a continuous number of procedures/blocks. The point at which shifts occur is easy to detect by an inflection in the plotted points. Is the slope on a CUSUM plot that indicates how average S differs from x.

Imagine you want to analyze your engine performance. By using the CUSUM system every time you input a record the graphic will update itself.
This way if you are getting better the slope of the graphic will slope down (negative) but if you "fail" the block the graphic will slope up (positive).

The graphic will continue to build up over time, depending on how many procedures you perform. Once your graphic starts moving constantly down we can consider that variations are under control.

In this case we have a representation of the data/blocks obtained by an aircraft engine during a period of time. A total of 59 blocks were plotted. You can see that from the very beginning this engine had a sustained performance. You can also notice that after 24 blocks engine data changed due to a different instance on the engine conditions. Then it had a very good run until at block 48 different conditions were identified, and then at 56 again. Because its tendency shows sustained performance the graphic becomes more and more negative with some positive slopes, but nothing really worrying. This engine shows a sustained performance under different operating conditions for the specific block. CUSUM sensitivity can be adjusted according to engine/fleet specifics in order to identify smaller or larger slope shifts.

A TeraSigma recommendation is to identify blocks from the CUSUM chart for a direct use on the run chart for the main and other relater parameters for a broader understanding on the engine performance/changes.

Contact us to discuss more on the use of CUSUM charts on your aircraft engine health monitoring.