Capability Calculations: Non-Normal Distributions and One Sided Distributions

N

Narfeldt - 2011

Capability: Non-Normal Distributions

Hello
I've just got an educatation in black belt and our teacher said (almoust) everything is normal distributed. And the whole course calculated on that. But in the real world I've have came in touch with other distributians like straightness off a calculated line, radial ran out.

How do I calculate capability on these types of distributians?

Sorry for my excelencs in English!

/Erik
 
L

Laura M

Excellent question. Did you cover one - sided distributions at all? Did you talk about the Central Limit Theorem? Even if an underlying distribution is not normal, the averages of subgroups tends to be normal. That's one reason control charts work for non-normal distributions.

As far as Cpk, there are probably better experts here in terms of theory. However, It drives me absolutely crazy to see "normal curves" drawn on very non-normal distributions because that's what 'the software does.' The normal distribution is a very specifc function that generates the normal curve. There are other types of distributions as well - exponential, logrithmic, etc. Each of these distributions have a calculation for standard deviation, based on the formula. (We're going way back into my Theory of Statistics classes now - hope I'm remembering correctly.)

A ways back, I generated a curve for leak test data - which was exponential. I ran a Chi squared test to establish correlation between the data I had and the exponential function I selected. This particular exercise was done to predict how many parts would be rejected at the limit versus those that were considered 'gross leakers' Without boring you with the detail, I was able to emphirically determine what reject rates of common cause variation was versus those that had a gross defect. Whether its called Opk or not, your data can talk to you in terms of whether the process has been improved. Perhaps you can construct the probability of a failure based on the data you have.

HOpe this helps.

Laura
 
D

Darius

Hi Erik

Welcome to the real word (it's a joke), :vfunny:

Most of what is written take "normal distribution" (gausian) in account, even mean it self is calculated with the same asumption.

It's for shake of simplicity, but in many cases is a good aproximation, I agree with you about non normality and it's my experience that, as Donald Wheeler wrote; "the central limit theorem has nothing to do with control limits", because the non normality of the range chart, and that the control limits are calculated with them.

Many practitioners will recommend to normalize data, but as the same autor said, most of the time, the chart loss the capability to be understand easily.

I readed an article that say that box-cox transformation is the best
"Computing Process Capability Indices for Non-Normal data: a Review and comparative study", by Loon Ching Tang and Su Ee Than; in the Quality and Reliability Enginnering International. Int 15: 339-353 (1999)

That article compares Wright's index; Clements' method; Box Cox transformation; and Johnson transformation.

Or use the "Yeo-Johnson Power Transformations" by Sanford Weisberg of the departament of Applied Statistics, University of Minnesota in Oct 26 2001

Or check for
"A capability Index for all Occasions" by K.S. Krishnamoorthi and Suraj Khatwani, that was exoposed in the ASQ's 54th Annual Quality Congress Proceedings; ussing a Weibull model.

You can still depend on non parametrical Capability index (also shown in the same article)

Cpu = (USL - median) / (X0.99865 - median)
Cpl = (median - LSL) ( (median - X0.00135)

You can still try to estimate variation to each side of the median (it's not written anywhere but I use it), and use the estimate to calculate the index.
 

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  • 2001crd119.pdf
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D

Darius

Tanks Sam, IMO Box-Cox is a good option, but is easer to rely on box-plot (as some practitioners does) or non parametrics; the difficult part is to estimate the precentile without the precence of outliers and with a small (relatively) sample.

I added a file that is more complete than the last (it is almost the same but I found that it touches some special isues), I didn't found it yesterday.

:thanx:
 

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  • SixSigmaSpecialTopics_GE.pdf
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