About this lesson
The CUSUM chart (Cumulative Summation) is a control chart that relies on historic process data when determining the values to plot. It can be easily created in either Microsoft Excel or Minitab.
When to use
Use the CUSUM Chart when monitoring a process for small shifts in the mean. The CUSUM chart requires variable data. The CUSUM chart also relies on a target value, so if the process has a target value that it is trying to achieve for business reasons, this chart will monitor deviations from that target. (Typically the target value used is the process mean.)
The CUSUM chart is an accumulation of the deviation of the subgroup mean from an adjusted target value. The idea of a cumulative summation is a very simple one, but this chart uses an important twist to the summation that often causes it to reset to zero. This twist is based upon the calculation of the deviation from the adjusted target value.
The key to this chart is understanding how this adjustment to the target value works. This adjustment is a sensitivity zone above and below the target value that is essentially considered to be equivalent to the target value for the purpose of calculating the deviation. This zone is typically plus or minus one half standard deviation above and below the target value.
The second feature of this control chart is that it is tracking both a high side and low side accumulation. These are referred to as one-sided accumulations since they are directional in nature. The control chart plot will include both summations on the same plot. Therefore, there are two data lines, but only one set of control limits.
There is a variation of this chart that calculates a two-sided summation and applies a V-mask to the chart. This variation is different in form from the Shewhart control charts and therefore, I do not recommend using it. I use the one-sided approach. The one-sided chart will be much closer to what your operators are used to seeing and working with.
Because of the way the cumulative summation is working, this chart will be able to detect small shifts to the mean faster than a Shewhart control chart. In particular, this chart is able to detect long term trends that might be lost in the noise of a system with high common cause variation until the mean had shifted dramatically.
The math for this chart is simple, but it is very important to keep the two cumulative sums separated and not combine or confuse them.
Within Minitab, control charts are created by using the “Stat” pull down menu, then selecting “Control Charts.” Within the Control Charts window, select “Time Weighted” and then finally select “CUSUM” In the Minitab CUSUM Chart panel, you will need to select the data columns with your data and set the target value. So for an existing process, you may need to first determine the mean value and then use that as your target.
If creating the CUSUM Chart in Excel:
- Determine the sensitivity zone and target value. The sensitivity zone is normally .5 times the adjusted standard deviations. The target value is often the mean of the process once it is stable. The chart is being used to ensure the process does not drift. The target can be a value other than the mean, but if it is not close to the mean of the data, the chart will quickly go to an out of control situation.
- Measure the attribute for the first item in the subgroup sample and record the data in a column in Excel. Then measure the next item in the subgroup sample and record that in the next column. By doing this, each row in Excel represents a subgroup.
- In an adjacent column, calculate the Mean for each subgroup and then in the following column calculate the subgroup standard deviation. If the subgroup size was one, this step is unnecessary.
- Calculate the adjusted standard deviation. The method used depends upon the size of the subgroup. The subgroup size will also determine the value of the constant.
- If the subgroup size is one, determine the absolute value of the Moving Range for each point (See the I-MR Chart). Take the mean of this value and divide it by the d2 constant.
- If the subgroup size is greater than one, Take the average of the subgroup standard deviations divided by the c4 constant and then divide that by the d2 constant.
- Calculate the sensitivity zone by multiplying the sensitivity factor times the adjusted standard deviation. The sensitivity factor is normally 0.
- Calculate the deviation value that will be added to the cumulative sum.
- For the high side cumulative sum, reduce the target value by one half the standard deviation when calculating the deviation value. Add that to the cumulative high side deviation. If the new cumulative sum value is less than zero, the new high side accumulation is zero.
Where K is the sensitivity zone – normally one half the adjusted standard deviation.
- For the low side cumulative sum, increase the target by one half the standard deviation when calculating the deviation value. Add that to the cumulative low side deviation. If the new cumulative sum value is greater than zero, the new low side accumulation is zero.
Where K is the sensitivity zone – normally one half the adjusted standard deviation
- Calculate the upper and lower control limits. These are just four times the standard deviation.
- Upper control limit = 4 x adjuseted standard deviation
- Lower control limit = -4 x adjusted standard deviation
- Plot high side accumulation, the low side accumulation and the upper and lower control limits. The chart will always have the Y axis centered at zero.
- Take appropriate actions to remove special causes or to center your data within the control limits.
Hints & tips
- This uses variable data, not attribute data.
- I find this chart is helpful for maintaining a process that is already under control.
- The data for this chart is normally collected in a subgroup size of one.
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