CUmulative SUM (CUSUM) chart

A cumulative sum (CUSUM) chart is a type of control chart used to monitor small shifts in the process mean. It uses the cumulative sum of deviations from a target.

The CUSUM chart plots the cumulative sum of deviations from the target for individual measurements or subgroup means.

The CUSUM requires two parameters:
  • A reference value (k) specified in sigma units. k is often set to half the shift to be detected, in sigma units. Default k=0.5 which is equal to detecting a shift of 1 sigma.
  • The decision limit (h) specified in sigma units. Default h=5.
When designing a CUSUM chart it is necessary to consider the average run length and shift to be detected. Extensive guidance is available on suitable parameters (NIST 2012, Montgomery 2012).

It is possible to modify the CUSUM, so it responds more quickly to detect a process that is out-of-control at start-up. This modification is done using an initial CUSUM equal to half of the h parameter.

Like the EWMA, CUSUM is sensitive to small shifts in the process mean but does not match the ability of a Shewhart chart to detect larger shifts. For this reason, it is sometimes used together with a Shewhart chart (Montgomery 2012).