# Analyzing Data with a Non-Normal distribution

C

#### Cognizant

Hi folks,

Recently one of our customers were questioning about our data was not normally distributed. we were concerned about cpks. but his concern was u cant analyse the data if it is not normally distributed...

my concern how cud u get the data normally distrribution.

C

#### Craig H.

One way to help aleviate this would be to use an X Bar and R chart instead of an XMR chart because a distribution of averages will be more normal, especially as n increases.

#### Statistical Steven

##### Statistician
Staff member
Super Moderator
Cognizant said:
Hi folks,

Recently one of our customers were questioning about our data was not normally distributed. we were concerned about cpks. but his concern was u cant analyse the data if it is not normally distributed...

my concern how cud u get the data normally distrribution.
Did the customer use any analytical tool to prove your data is not normally distributed? It might be true that your Cpk values are biased by the nonnormality, but first you need to have a statistical test that does not accept normality. Try the Wilks-Shapiro method, Kolmogorov-Smirnov method or just a normal probability plot.

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
Interesting how much concern there is over normality of late.

SPC does not depend upon normality. Shewhart did simulations with several skewed distributions. Wheeler has also done work with various non-normal distributions and found SPC works even if the data are not normal.

Myself, I am not a believer in using CpK. Much better to judge from the control chart itself how the system is performing and if its results are predictable or not.

If normality absolutely is an issue, then yes you can study the data to see if it normal or not, and if really really necessary one could develop a mathematical transform in order to shift the data to normality.

Another option is to shift to non-parametric analyses.

Last edited:

#### Statistical Steven

##### Statistician
Staff member
Super Moderator
Steve Prevette said:
Wheeler has also done work with various non-normal distributions and found SPC works even if the data are normal.
I think you meant to type if the data are NOT normal.

I do not like Cpk either, but with the 6S craze, people want a single metric that describes their process. Given that, you can report a Cpk, but I do not hold to the 1.33 or any other rule as a good process.

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
Statistical Steven said:
I think you meant to type if the data are NOT normal.
True. I went back and edited the post.

C

#### Cognizant

NOt normal distribution

Our data failed the normal distribution on many key charactericstics...for example one part key characteric thickness .013+/-.001(inches) thickness Rockwell 50 ..our boss always orders the material at .0135 RC50 because he can't find material at .013 and RC 50...and all the data points are around .0135...this ultimately lead to a non normal distribution with 6 pack Minitab R14... and we said this is what it is nothing can be done to make the data Normal......

This is just one example ...there are many other key characteristics which are not normally distributed...we always go with Cpks and Ppks but our customers says u cannot go for Cpks and Ppks without the normality test ....then we asked are there any tools to use non normal data..he said he was not sure ...

I am sure Minitab provides solutions both for normal as well as not normal distributions....but my concern is which one to use...Our data sometimes lead to normal distributuion and sometimes to not normal distribution on some characteristics.....

Thats our major customers concern ..Y the data s not normal??????

Thanks for answering folks..I'd really appreciate it...

#### Jim Wynne

Staff member
Cognizant said:
Our data failed the normal distribution on many key charactericstics...for example one part key characteric thickness .013+/-.001(inches) thickness Rockwell 50 ..our boss always orders the material at .0135 RC50 because he can't find material at .013 and RC 50...and all the data points are around .0135...this ultimately lead to a non normal distribution with 6 pack Minitab R14... and we said this is what it is nothing can be done to make the data Normal......

This is just one example ...there are many other key characteristics which are not normally distributed...we always go with Cpks and Ppks but our customers says u cannot go for Cpks and Ppks without the normality test ....then we asked are there any tools to use non normal data..he said he was not sure ...

I am sure Minitab provides solutions both for normal as well as not normal distributions....but my concern is which one to use...Our data sometimes lead to normal distributuion and sometimes to not normal distribution on some characteristics.....

Thats our major customers concern ..Y the data s not normal??????

Thanks for answering folks..I'd really appreciate it...
The fact that the data is centered around .0135 and not .0130 doesn't mean the distribution isn't normal. In fact, because you're referring to some sort of material thickness, I'd bet that the distribution is normal. So what do you mean by "not normal"?

#### Statistical Steven

##### Statistician
Staff member
Super Moderator
Jim Wynne said:
The fact that the data is centered around .0135 and not .0130 doesn't mean the distribution isn't normal. In fact, because you're referring to some sort of material thickness, I'd bet that the distribution is normal. So what do you mean by "not normal"?
Might also fail because of a lack of gage discrimination. But, I agree noncentered in the specification does not imply nonnormality.

C

#### Cognizant

Msa

I mean .0135 is not normal in the sense ...example ..I have the data of 50 pcs

20 pcs were .0133
25 pieces were .0134
5 pieces were .0135

this is not normal data at all...it fails the normality test....

I am guessing its probably the measurement system ..
It needs to be more accurate reaching upto millions 5-7 decimal places...
But I can't get that accurate data with ball mics.....I have to use some kind of optical measuring system for which my boss never agrees to buy......

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