# Normality Test

Six Sigma – iSixSigma Forums Old Forums Europe Normality Test

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• #24042

Nusha Safabakhsh
Participant

If a set of continuous data is not normal; however, a group of daily average for the same set of data is normal, does it make sense to use the average of analysis and creating control chart?

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#57570

Participant

Of course it is. That is how control charts work. It is called the central limit theorem. Regardless of the underlying distribution, averages of samples from the distribution will approximate a normal distribution.

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#57571

Olga Kolburt
Participant

I did this and everything on the control chart, this case an X-bar R chart subgroup 5, look fine, however when conducting a normality test for the individual observations, the data are not normal. Based on this fact I should not compute the Cpk because data are nonnormal.
Can someone explain the dilemma, the distribution of the means is normal (the child distribution  is normal) the individual observations (collected on subgroups of 5 are not normal (parent distribution is not normal) when calculating Cpk, should I transform the data?
Olga Kolburt

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#57572

Participant

Hi Olga,
You can’t change the underlying distribution. This happens. As I said, that is why control charts work for averages.
Regarding calculating the CpK: Assuming that your data is not being influenced by some special cause, I suggest using an SPC package that applies Pearson curves to fit the data. They can calculate the CpK for you. For me, if my data meets the basic Camp-Meidell requirements, I would just use the standard CpK.
Are you using the range to estimate the standard deviation here? Try calculating the CpK by using the standard deviation of the individuals (PpK).
There could be several problems with your data. Two common ones are mixed production streams and time related factors.
The first is caused by mixing a high and low value together in every sample. An example might be taking one piece from each of 5 cavities of a die. You can see this on the chart if the X-bar hugs the centerline and the R chart looks in control.
The second case occurs where set-up variation or tinkering occurs in your process. Sometimes it is due to tool wear. The can be seen on the control chart by having an in-control Range chart and frequent points outside or near the limits or runs on the average chart.

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#57573

Olga Kolburt
Participant

Thank you Mike for taking the time to provide enlightment.
I would review my data to understand wahy the data are not normal.
While looking for SPC software, I found a discussion from Statit, which states: “What is normal and how normal does a distribution need to be for a control chart to be effective? The answer, surprisingly, may be not very.  The article is available at:
http://www.statit.com/support/quality_practice_tips/discussions_on_normality.shtml
Once again thank you for your help.
Olga

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#57580

Scott
Member

Hi, Nusha. You see, the Central Limit Theorem rises again. Let me know if you need more help.

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