MINITAB and non-normal unilateral tolerance data - Cannot confirm Ppk values

[VMax!]

OK. I downloaded/installed v14. Input the data. Ran Quality Tools/Individual Distribution Identification. The charts represent 'best fit.' Extremely low or nonexistent P values. AD ranged from 16.4 to 2.8.

Q: For non-normal distributions (specifically parallelism), are there threshold numbers for P and AD? Why/why not. I have been taught for normal distributions, AD<0.752 and P>0.05. Is there a similar 'rule-of-thumb' for non-normal data?

In this example, 3-Parameter Gamma contains all the points and has the 2nd lowest AD value. 3-Parameter Lognormal has the lowest AD, but some of the data points are outside the lines.

Q: Should I base the next step (Capability Analysis/Nonnormal) on the graph or the values of AD and P? I've tried it both ways (3-P Gamma and 3-P Lognormal). Similar Ppks.

I included that data - link above. 230 data points.

 

[pabloquintana]

Extremely low or nonexistent P values.

VMax. I tried your data. If P-Value is less than alpha then none of the proposed distributions fit your data.

What I would do is go with a Box Cox transformation in Normal Capability and get your info.

What is your upper limit?

Pablo

 

[VMax!]

If P-Value is less than alpha then none of the proposed distributions fit your data.

OK. Thanks for the tip (and taking time to review my data). Tried Box Cox Transformation and got this error:

* ERROR * All data must be positive when using the Box-Cox transformation.

I changed my data (replaced the 0's with 0.0001) and finally got the Box Cox to spit out a graph. Is this permissable?! The USL is .009.

 

[Miner]

OK. Thanks for the tip (and taking time to review my data). Tried Box Cox Transformation and got this error:

* ERROR * All data must be positive when using the Box-Cox transformation.

I changed my data (replaced the 0's with 0.0001) and finally got the Box Cox to spit out a graph. Is this permissable?! The USL is .009.

No. If you have to change numbers from zero to make the distribution work, you are breaking a primary assumption of the distribution, which proves that the distibution does not apply.

I used Minitab to run an Individual Distribution Identification. Four distributions offer potential answers (3-parameter lognormal, 3-parameter Weibull, Largest Extreme Value and 3-parameter Gamma) by the Anderson-Darling statistic. The low p-value rules out the 3-parameter Weibull; the probability plot rules out the Largest Extreme Value; and, the probability plot is very questionable for the 3-parameter Gamma.

The best fit based on A-D, p-value and the probability plot appears to be the 3-parameter Lognormal distribution.

You can then use a non-normal capability analysis using the 3-parameter Lognormal distribution with 0 as a lower Boundary and .009 as an upper spec. This gives a Ppk = 1.09 and an expected 863 PPM overall performance.

 

[pabloquintana]

I changed my data (replaced the 0's with 0.0001) and finally got the Box Cox to spit out a graph. Is this permissable?! The USL is .009.

VMax, I don't find it a big issue. You are simply using a small number that is not zero but very close to zero to allow the Box Cox transformation to run.

Compare the results with what Miner said in the previous post.

Pablo

 

[Darius]

I don't have any stat pack but I checked with X^0.5 and the standard deviation looks almost the same both ways (up and down), the ppk that way is 1.2. The box-Cox obtain the exponent for the X, so it looks like 0.5 to me (in your set of data).