Recently we had a number geometric features from our machine shop that had been reported as being incapable (0.51).

Upon investigation the SPC software had fitted the data to a FND - which with research appears to be correct. I understand that the FND is used where the data is normally distributed but also has a natural boundary (i.e 0) - which is the case with our feature / process.
However when you fit a Normal distribution model (the data is normally distributed) to the data the process is capable (Cpk 1.30) - see attached.

The problem I have is convincing our Shop Floor - and to be honest myself - that a FND is the appropriate model to use.

Theoretically you might expect a geometric feature to be right skewed in shape and therefore fit a non-parametric model. What is the logic to fitting a FND to geometric features (i.e Flatness, Squareness, Parallelism, etc)?

I'm probably being a bit dim here but if someone could help I'd appreciate it.

Thanks in advance

Steve

Just looking at it visually, I'd say the regular normal distribution is a better "fit" to the data than the folded. You could statistically analyze which is better by doing a chi-square goodness of fit test.

Is the LSL really zero or are you really dealing with a one sided specification?

If you are really worried about the termination of the normal at zero, you could try using a other distributions such as the Weibull or Beta. But, I don't think you really have an issue there.

I agree with Steve:
Just looking at it visually, I'd say the regular normal distribution is a better "fit" to the data than the folded. You could statistically analyze which is better by doing a chi-square goodness of fit test.

If you'd provide me with your data set I'd be happy to run it through our GainSeeker Suite and give you some alternative analysis.

Evan should have clearly stated (per the TOS) that he is the owner of the company that owns and sells GainSeeker Suite. Essentially this post is self promotion for his product.

If you are really worried about the termination of the normal at zero, you could try using a other distributions such as the Weibull or Beta. But, I don't think you really have an issue there.

I agree, although a snapshot of the process may fit the curves your software suggests, but I believe their actual behavior is closer to Weibull. The further from zero (the worse you are) the more 'normal" you get. The closer to zero (the better you are) the less 'normal' and more skewed you get. It is like watching a normal curve hit a brick wall. So, if it is normal, it is not as good of a thing. :cool:

Theoretically you would expect to see geometric features to be skewed to the right but as you know processes are 'real' and sometimes just don't act the way we either expect or might wish them to.

We ran the dataset via Minitab to test the fit and it suggested either a Normal and Logistic distribution would be the 'best fit's' (Minitab doesn't appear to have the option to test for FND). Incidentally the software we use of the shop floor also performs an automatic GoF test - hence the FND being its 'best fit'

With regard to it not being an issue I'm more concerned about the reported FND and its use rather than the process itself. Yes, you could argue that if we ran additional analysis or even calculated by hand that you might get the result / fit we're looking for but with nearly 3000 process to assess we have to rely on statistical software and what it tells us.

We do have the option to remove the FND option from the GoF test - which when we do returns a Normal distribution. However this begs the question as to whether we're 'forcing' the dataset to fit what we want rather than what it is?

I have attached the dataset for those kind enough to offer.

Once again thanks in advance

Steve

Assuming the data are in the time sequence that they were produced, you do indeed have a problem - the data are NOT stable. There is a recent increasing trend which should be looked at (red circled).

I should point out that distribution fitting and Cp anlayses are meaningless if the data are not stable and predictable.

I would not expect a form feature to be "stable". What we find is that the form data is relatively stable until the tool wears to the point that there is a sudden increase in tool pressure. This is why when utilizing the X hi/lo-R chart for precision machining diameters or lengths that the range chart (roundness or parallelism) is a leading indicator of the need for a tool change. I am also betting a good deal of the variation seen in this data is measurement error - although difficult to verify from a distance. :cool:

Thanks for your comments guys, they are appreciated. However I'm still left with the question of why a FND is used to model unilaterally toleranced form features?

Any takers?

Maybe they derived its use from a reference like this:

http://www.jstor.org/pss/1266560

Hmmm....have to read it.....:read:

Steve is right on.

Assuming the data are in the time sequence that they were produced, you do indeed have a problem - the data are NOT stable. There is a recent increasing trend which should be looked at (red circled).

I should point out that distribution fitting and Cp anlayses are meaningless if the data are not stable and predictable.

I attached some output from GainSeeker Suite which corroborates his conclusion. GainSeeker automatically flags it as a normal distribution, but as Steve points out distribution fitting and capability analysis are meaningless because of the stability issues.

Regarding your question about why your software is using the FND to model the unilateral tolerance dimension - my comment as a commercial software developer is predictable: that software doesn't know any better. We have a slightly different approach and I'd be happy to share it with you.

Evan should have noted (per the TOS) that he is the owner of the company that owns and sells GainSeeker Suite. Essentially this post is self promotion for his product.

Thanks for your comments guys, they are appreciated. However I'm still left with the question of why a FND is used to model unilaterally toleranced form features?

Any takers?

First off, I don't know who actually is using, or recommends using a FND. I have a Masters Degree in Operations Research, and read quite a few statistical texts, but have never run across it before this discussion.

Usually I see folks make use of Weibull, or some form of Beta or Gamma distribution if they do have a distribution with a natural lower limit. I should point out there are also ways to deal with this using a truncated normal distribution. I suppose the FND is a truncated normal that happens to be truncated at the median.

If the data were monotonically decreasing from zero, the FND (truncated normal at the median) could be useful. But that does not appear to fit your data.

HOWEVER, while we are on the discussion of fitting data - IT WOULD BE VERY DANGEROUS AT THIS POINT TO FIT ANY DISTRIBUTION TO YOUR DATA. Your data are not stable and predictable. Either due to tool wear, or some other issue(s) there are significant trends in your data. Any attempt to fit all 150 points against ANY distribution would be fool-hardy. First the process must be brought into stability, or dealt with as tool wear if that is appropriate. Then we can talk about the best statistical model to predict results with.

Any attempt to fit all 150 points against ANY distribution would be fool-hardy. First the process must be brought into stability, or dealt with as tool wear if that is appropriate. Then we can talk about the best statistical model to predict results with.

Yes, plugging data into a curve finder without understanding the underlying variation is rudimentary. What is the total variation? For flatness we have measurement variation, tool wear variation and accompanying tool pressure variation, material variation, tool lot variation, etc. For their contribution, what is the underlying distribution of each, and the degree of their participation? If you can find a curve fitting software that can derive that information, then you may have something handy. But, it is yardstick to see what neighborhood you are in, not a final measure of the behavior of your process. :cool:

Originally Posted by Steve Prevette

First off, I don't know who actually is using, or recommends using a FND. I have a Masters Degree in Operations Research, and read quite a few statistical texts, but have never run across it before this discussion.The FND is widely use in the French standards (CNOMO / Q544000) developped by french car manufacturer (Renault / PSA). The FDN is used for what they called "Form Defect" (Literral translation from french, or form feature as bobdoering said) for example : circularity, perpendicularity, ...

And from my little experience, i can tell you that the only place where i have seen the FND distribution used is in France.

These French standard doesn't have exactly the same approach to SPC than "QS9000". But the goal is the same.

Perhaps UkSteve using a french SPC software :D

I hope my english is comprehensive.

Perhaps UkSteve using a french SPC software :D

I hope my english is comprehensive.

Geographically you're next door - the software is German and as I understand it used by many of the European car manufactures. Incidentally your English is fine at least compared to my French :D.

Steve / Bob
Before I come across as being statistically negligent, we were aware of the instability issue and as such has not been overlooked, we just wanted to understand the use of FND in this instance.

Bob
Thanks for the link

My suggestion would be to establish your baseline distribution with a new sharp tool, perhaps over the first 3rd of the tool life. Your data is far enough away from zero that I would expect the variation to be normal. Still pondering measurement error, though. It will definitely be a normal distribution contribution to the total variance. Then look for the change from that - which may be what you are seeing in the longer term sample - as a signal that the tool may need changed. The "instability" may be a special cause looking for a reaction (for lack of better explanation), and should not be included in the evaluation.

Just a suggestion from a distance. :cool:

One tool I used to evaluate the distribution of the data you collected is "Distribution Analyzer" (http://www.variation.com). It determined that the distribution closest to the data you supplied was a Gamma Distribution (see attached). It was not that different from the normal distribution (also attached), which is what I suspected for how far from zero your data set lied. Had your flatness been better, the normal distribution would not have fared well in the analysis. As I mentioned before, the worse you are in a unilateral tolerance, typically the more normal you are.

You can use the information as a starting point for your process analysis. :cool: