# Non-normal Distributions in Statistical Process Control

A

#### Andrews

Non-normal Distribution

Are there any websites that contains useful articles, materials on the subject of Statistical Process Control, in cases where the distribution is non-normal?

R

#### Rick Goodson

Andrews,

There is an excellent article titled "Process Capability Indices and Non-normal Distributions" that was published in "Quality Engineering" in 1996 or 1997. The authors are Steven Somerville and Douglas Montgomery. Somerville is (or at least was at the time of the article) employed at TRW in Mesa, Arizona and Montgomery works in the Department of Industrial and Management Systems at Arizona State University. You can purchase the paper from ASQ through their website. I belive the cost is about \$10.00 or so.

Regards,

Rick

R

#### Ravi Khare

Non normality

Is there a non-parametric way of evaluating Process Capability? That way you don't have to worry about the shape of the distribution.

D

#### Darius

Ravi, the method recommended for non-normality if you are not using a data transformation (like box-cox) is using the median, the 99.5th and the 0.5th percentile of the data.

"What happens if the process is not normally distributed?"

http://www.itl.nist.gov/div898/handbook/pmc/section1/pmc16.htm

T

#### Tom Slack

If the data isn't normal, does it have a different distribution? Finding it would be quite valuable and would make limits easy to determine. Use nonparametric methods as a last resort because increasing sample size is usually necessary to compensate for the loss of power.

Should the data be normal? This could be answered by a process engineer. If the answer is yes then look for causes. Often there are causes that are not economical to control, such as seasonal changes. There are ways to get around it. The term usually associated with these techniques is called "Rotating Data".

Hope this helps.

Best Wishes,

Tom

R

#### Ravi Khare

Tom Slack said:

There are ways to get around it. The term usually associated with these techniques is called "Rotating Data".

Hope this helps.

Best Wishes,

Tom

Tom,

This sounds interesting. Can you please elaborate? How does one 'Rotate Data'?

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T

#### Tom Slack

Ravi,
Think of a regression line through data. Now "rotate" the data around the mean until the slope is zero. This would be easier to explain with a pencil and paper. :>> After the data is rotated (or transformed), it would be easy to determine control limits.

I hope that explanation helped. I am not in favor of rotating data because it hides things that are going on in the process.

Best Wishes,

Tom

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