A CUSUM chart is used to look for small shifts from a target. There are two types of CUSUM chart that Minitab will generate: One-sided CUSUM charts, which we will use here, or the two-sided or V-mask CUSUM.
CUSUM charts like EWMA charts can be useful when subgrouping of the data for an Xbar chart is not feasible and the I-MR chart is not sensitive enough. These may include scenarios where we have low production volumes, or where sampling can be prohibitively expensive or potentially destructive.
The data in this example looks at the fill volumes of syringes. There is a target volume of 15 ml. We will plot the CUSUM using a subgroup size of one to identify deviations from this target.
The following steps will generate a CUSUM for a target of 15 and a subgroup size of 1:
- Use Open Worksheet… from the File menu to open the
Volume2.mtwworksheet. - Navigate to Stat | Control Charts | Time-Weighted Charts and select CUSUM….
- Enter
Volumeand enter Subgroup size: as1and the target as15. - Click on OK to create the CUSUM.
The default plan type is the one-sided CUSUM. This plots two lines. The top line detects upwards shifts from the target and the lower CUSUM detects downward shifts. The type of CUSUM can be changed in CUSUM Options and the Plan/Type tab.
The values of h and k for the CUSUM plan affect the sensitivity of the CUSUM. In a one-sided CUSUM, h, the decision interval is the number of standard deviations between the center line and the control limits. The value of k affects the drift to be detected. Default figures of h and k are 4 and 0.5.
The Plan/Type tab also has options to select Fast Initial Response (FIR) and the two-sided CUSUM can be centered on a given subgroup.
The results can be compared with an I-MR chart using a historical mean of 15. By looking at the cumulative sum away from target, the CUSUM becomes more sensitive at identifying the small shifts away from target.