Basic question regarding CUSUM SPC Charts in JMP

[#1]

@martindemel

CUSUM charts in JMP are based on the target and the sigma values, which are being calculated by JMP. In my understanding, the target value is the mean and sigma is the standard deviation of the data set.

However, JMP generates values which are different to the mean and the standard deviation.

I'm wondering what JMP is exactly calculating. The following JSL shows the differences:

Names Default To Here( 1 );
Open(
	"$SAMPLE_DATA/Quality Control/Engine Temperature Sensor.jmp"
);
CUSUM Control Chart(
	Y( :Y ),
	Target( 100 ),
	Sigma( 10 )
);

Tabulate(
	Show Control Panel( 0 ),
	Add Table( Row Table( Analysis Columns( :Y ), Statistics( Mean, Std Dev ) ) )
)

Any in depth information’s are very well come. Thanks.

[#2]

Please see the JMP CuSum Chart Help pages.

[#3]

To add to @Mark_Bailey's good advice, there are a few issues here.

First, your script is specifying the target and sigma values. But I see what you are saying. The default target is 103.963 with a sigma of 10.9792. The 103.963 is correct. Your Tabulate output is using the default format of 5,Best. Change the 5 to something bigger, like 10. You will see that the mean truly is 103.963. Tabulate was just rounding the result to fit the specified format.

As for the sigma, as the help pages state, sigma is estimated by using the moving range, not the traditional standard deviation formula.

[#4]

The JMP Help for the CUSUM contains the Statistical Details

They can be accessed through the Help tool "?" in JMP or clicking Here 

[#5]

I did check out the JMP help

https://www.jmp.com/support/help/en/16.1/#page/jmp/statistical-details-for-cusum-control-chart-const...

for CUSUM. What I found was:

• T is the target of the process
• σ is the standard deviation of the process

Am I missing something?

[#6]

Could you be confusing 'target' and 'mean'? The target is specified by you. The mean is calculated from the data on a subgroup basis.

[#7 · Accepted solution]

When building the CUSUM Chart with this data from scratch, you get a target of 103.963, which is the mean of the data. As you do not have spec limits set this is the default. If you have specs set it would put in the target of the spec setting or the mean of the upper and lower limit. 

Now the sigma is different. It will be 10.9792 , which differs from the standard deviation. Thats because the sigma used here is not the standard deviation from the data itself (like in a levey.-jennings control chart) but the moving average sigma from a control chart. 

Here you find this example in more detail in a blog post: https://community.jmp.com/t5/JMPer-Cable/How-to-detect-small-shifts-in-Control-Charts/ba-p/49452  and in the documentation for JMP 16.1 (or search in the future JMP versions online documentation for "Control Panel for CUSUM Chart": https://www.jmp.com/support/help/en/16.1/#page/jmp/control-panel.shtml 

@AnnieDudley may add or correct my statement

[#8]

@martindemel is correct. The default sigma for the CUSUM Control Chart is calculated using the moving range, as recommended by Prof. Bill Woodall. He advises against using a traditionally calculated standard deviation for any cumulative or moving average chart, including CUSUM charts.

[#9]

Thanks for the addition info. Am I Right in guessing that that moving average data are being used on order to have a more up to date target and sigma value, or in other words to suppress the impact of older data?

[#10]

Hi Thomas, not exactly sure, but I would rather say, the goal is to detect small shifts you cannot detect that easy with typical control charts. Large special cause variation can be seen easily but may hide small shifts. So averaging these large spikes out will probably provide a fairer assessment of a small shift. 
I do not have any reference and am also no per se expert in CUSUM charts, but that's what I conclude thinking about it. Happy to remove this thought in case this is wrong.