Q 432. In Statistical Process Control what is the advantage of using a Cumulative Sum (CUSUM) chart over a more traditional Individual or X-bar chart? Highlight the advantage using the same data.

 

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One of the types of control chart is cumulative sum (CUSUM) chart which is used to monitor small shifts in the process mean. The cumulative sum of deviations are used from a target. The purpose of this chart is to check if the process is on target or not. The CUSUM chart plots sum of the deviations of samples or subgroup means from the target. The CUSUM chart found to be extremely useful in identifying small shifts in the process mean.

On comparing the CUSUM chart with the traditional chart, the former helps in detecting the small change in process mean while latter is to monitor the process within the control limits and indicating any impact of process improvements. Though, all processes will have drift in the mean but If small shifts in the average isn’t of that importance then control chart would work fine otherwise, CUSUM chart would be helpful if there is no scope of minute error in the process.

Since CUSUM control chart works on sum of deviations versus the actual values of the process being used in the individual control chart, the disadvantage of CUSUM chart is seen that underlying data of process is being lost.

The CUSUM chart is used to detect very small shifts to the process. It is able to detect these small shifts because it incorporates the data from the sequence of the sample. It plots the Cumulative SUMs of the deviations of each value in the sample from the laid down target. These deviations should vary randomly above and below zero. A trend in either way would indicate a shift in the process mean. Being cumulative helps in the detection of very minor drifts to the process mean and will either cause a steady increase or decrease in the cumulative deviation values. The sample values can be individual measurements or the means of the subgroups. In case we do not want to detect very small shifts, variables chart for subgroups such as the Individual-MR Chart or the Xbar-R Chart. In case the data is the count of defects/defectives, the U or P Chart can be used.

Example

A quality engineer at a plant that assembles automobile engines monitors the movement of crankshafts in the engines. In an operating engine, parts of the crankshaft move up and down a certain distance from the baseline position. The engineer took five measurements per day from September 28 through October 15 and then 10 per day from October 18 through 25.

The example of the same data displaying a CUSUM Chart and an Xbar R Chart shows that while the X-Bar R Chart is in control, the CUSUM Chart is able to detect the minor shift in the process mean indicated by the red dots in the control chart.

References

https://support.minitab.com/en-us/minitab/18/help-and-how-to/quality-and-process-improvement/control-charts/how-to/time-weighted-charts/cusum-chart/before-you-start/overview/

https://support.minitab.com/en-us/minitab/19/help-and-how-to/quality-and-process-improvement/control-charts/how-to/time-weighted-charts/cusum-chart/methods-and-formulas/methods-and-formulas/

Example Data from support.minitab.com

https://support.minitab.com/en-us/minitab/19/help-and-how-to/quality-and-process-improvement/control-charts/how-to/time-weighted-charts/cusum-chart/before-you-start/example/

Advantages of CUSUM chart over Individual, X BAR chart

 

1. CUSUM chart is used to detect smallest variation from target value. This chart is used where sub grouping is not required / feasible, however, there is a need to detect very small shift (less than 1.5 sigma). The biggest advantage is that the user can determine the degree of shift that needs to be detected

This type of chart can also be used where the process average is expected to naturally shift, for e.g. chemical industries

2. This chart is a better choice when the objective is to control the data point to a target value by making necessary process adjustments than plotting an X Bar or Individual chart and then trying to identify special causes for variation

Example using data (reference source from Cumulative Sum Chart (CUSUM) - Six Sigma Study Guide)

Minitab or other SPC tools can auto calculate the upper and lower CUSUM for all values

 

 

CUSUM chart shows that the process is deviating from target from sample 13, whereas, the below IMR chart shows that process is in control and is stable. Hence CUSUM chart is more useful to detect small changes in the process mean compared to X Bar and I MR charts

 

During the control phase of the project, we sometime want to check how the small shift is going to impact the process target. We need to use Cumulative Sum (CUSUM) in these scenarios. It is the sum of deviation of individual sample or subgroup average from the target. These cumulative deviations over time are plotted in the CUSUM control chart and this clearly help us to identify when the process if out of control.

 

As we are aware, the X-bar helps is also a control chart which monitors the average or the mean of the process and how it changes over time.

 

Below are some of the distinct differences between CUSUM Chart and X-Bar Chart:

 

CUSUM Chart	X-Bar Chart
Monitors the quality of a stable process when the expected shift is small	Monitors the movement of average of the process over the time
Used when there is high cost of false alarm	Used when there is low cost of false alarms
Used when there is high cost of repairing a process	Used when there is low cost of repairing a process
Faster detection of drift in the process with same sample size	Takes almost double the time to find the drift with same sample size
Subgroup size is generally 1	Subgroup size is generally 5

There are only 2 answers that have shown the differences between a regular control chart and CUSUM chart, making my job that much easier 

 

The best answer to the last question of 2021 has been provided by Gopal Menon. 

 

Read Johanan's answer to look at another example and Sandip's answer for a tabulated comparison.