# Bootstraping and Resampling Statistics - Capability for non-normal variable data

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#### Ravi Khare

Any experts around who can help?

Thanks.

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#### Rick Goodson

It appears none of us have any experience in that area. I'll look around and if I can find any leads I will email you.

Rick

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#### Atul Khandekar

Non-parametric

The entire theory & practice of SPC is heavily based on assumptions of 'normality'. However, in reality many of the processes are 'not normal'. Common practice is to use transforms to convert the data into an 'equivalent Normal' distribution.

I am looking for some information on what non-parametric methods are available, if any, for computing process capability regardless of distribution.

Can anyone provide any pointers to info on web / books?

Thanx,
-Atul

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#### BRoyal

You might try Davis R. Bothe's book "Measuring Process Capability," McGraw-Hill publishes it. ISBN is 0-07-006652-3.

The book has a chapter on measuring capability for non-normal variable data.

Good luck.

Ben

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#### Rick Goodson

Atul,

Take a look at the Weibull distribution as an alternative to the normal for estimating process capability witha non-normal distribution. The cumulative distribution function can be used to determine the portion of the distribution that exceeds a limit.

Dr. Donald Wheeler presented a paper at the 1991 ASQC Congress called "Shewart's Charts: Myth, Fact, and Competitors. It had some good information in it also. Unfortunately I can not find my proceedings or I would send you a copy. You might try his website Dr. Donald Wheeler for a lead on the proceedings.

Regards,

Rick

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#### Atul Khandekar

Why distribution?

Thanx Ben and Rick. I'll look up the references you suggested.

Do we have to classify the data in distributions - normal and non-normal? Is it possible to work with just the numbers without trying to fit a distribution (non-parametric) and still calculate the process capability?
-Atul.

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#### Atul Khandekar

This is one of the responses I have recieved from an other source:

"...Even with highly nonnormal data you're usually OK if you're using X-Bar R or X-Bar S charts, because the Rule of Averages takes care of the nonnormality (i.e since you're plotting averages instead of raw data, and averages are normally distributed, uou're OK). With variables charts, there's really only a problem when using Individuals charts - a nice solution to nonnormality there is to use EWMA charts instead of individuals charts. Again, since EWMA charts use averaging the points that are plotted become approximately normally distributed..."