I am a mechanical engineer recently thrown into the SPC arena. I know little or nothing about the subject, but have been reading voraciously. I have started to gain a basic understanding of the topics, however, I can find no literature that connects GD&T to SPC. I am primarily interested in Cpk. My problem is that I don't know if Cpk is the correct index. Most of the parts are machined and we have developed key characteristics. The problem comes in trying to figure out the math. Any help will be greatly appreciated. Thanks.

I can find no literature that connects GD&T to SPC.

Yea, that would be sorta tuff. Most traditional SPC text rarely takes GD&T into account because SPC is supposed to focus on the process aspect of the operation. However, there are some statistical aspects to GD&T. Chapter 11 of Grant and Leavenworth's Statistical Quality Control and Chapter 23 of Juran's Quality Control Handbook cover the topic rather well. If you do not have these books, visit a library. A local college or university should have them.

My problem is that I don't know if Cpk is the correct index.

Visit here and download the file CPK.PDF. Read thru that and if you have any further questions, ask.

http://Elsmar.com/pdf_files/

There are other good files there as well that may be of some help.

Regards,
Don

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Just the ramblings of an Old Wizard Warrior.

Thanks for the info.
When I finish reading all of it, I'm sure that I'll have more questions.
After all, the hardest part of a long journey is the first step.

Just stop back by and ask your questions and we (particularly Don - our local statistical wizard) will try to help out.

[This message has been edited by Lassitude (edited 29 July 1999).]

Sometime back, I received a paper on that very subject. I will try to find and forward. Stay tuned.

Regards,
Don

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Just the ramblings of an Old Wizard Warrior.

Ok, I've done some reading and feel like I'm starting to get a handle on some of this stuff. I am having some trouble finding a way to determine my USL and LSL values when applying the max material condition modifier to hole locations. As you all know, the MMC modifier allows bonus tolerance to hole position based on the hole size. How can you come up with a mean and standard deviation when the allowable values float directly proportional to feature size? My brain is almost fried on this one. This statistical stuff is more than a gear head can comprehend.

Interesting question. My brain keeps racing over Virtual Condition (worst case condition). I am thinking that this would be your tolerance range when figuring your Cpk. What do you think Don?

I have found the paper that demonstrates the Cpk calculation for MMC. I admit I find it interesting. The paper is in PowerPoint 4.0 and I can forward to anyone who is interested.

Regards,
Don

Don,

Please send it my way. I would like to give it a read.

Regards,

Kevin

I have given the paper a once over. At first glance it appears to have solved my problem. I really appreciate everyone's input. As I get deeper into the application I'll let everyone know how it's going. A particular thanks to Don. The paper was a real life saver.

particularly Don - our local statistical wizard

Thanks for the kind word words. I appreciate it.

This statistical stuff is more than a gear head can comprehend.

Years ago, I was a fixture, tool and jig designer for the company I worked for at the time. If I had thought at the time I would be in this field, I would have said no way. Time does change things, don’t it. Stick to it.

A particular thanks to Don.

I do not know if I would go that far. I did not author the paper and there should be thanks to the author. I just forward the information I have and hope there are those that can use it. I had never heard of MMC before this paper.

Regards,
Don

http://Elsmar.com/gif/druid.gif

Don,

Do you know what you want to be when you grow up yet (LOL)? Funny thing, life. The direction I picked out in my teens is much different from the course I am on today. I believe this is true for most folks. Chances are, I will shift again at some point.

Statistics is an interesting subject, which, in my teens, I hadn't an interest. I realize today that life is made up of a multitude of processes. Business, no different. As in life and business, the choices we make are still ours. Better to make choices based on accurate, predictable processes. I believe the use of statistics (basic or advanced) helps to make folks make better decisions.

Through heavy mathematics in college, I still did not dabble with statistics, and their powers were still beyond me. Only after being introduced to SQC in a follow-up college course did I begin to understand their powers. Subsequent studying for the CQE, I built on the foundation. After reading several Deming books, I am convinced in their powers. My understanding of Statistics: I would consider myself a novice, desperately not trying to become a hack. But I agree with you Don, we are never too old (not smart enough) to enjoy a change.

Regards,

Kevin

Do you know what you want to be when you grow up yet...

Not really. Just an Old Wizard trying to find his way.

BTW, I have forwarded about ten or twelve copies of this thing. I ask only that if those I have sent it to forward it to someone else, please credit the author. As I stated above, it was not mine and will not nor want to attempt to take credit for it.

Thanks all.

Regards,
Don

http://Elsmar.com/gif/druid.gif

This is really a long story so I'll try and give the condensed version while attempting to provide enough detail to still make sense. I work as a consultant to the government for engineering issues. The contractor that provides our system has started to implement SPC. We put this effort on contract with advice from another consultant. He specified Cpk as the capability index. The contractor has been negotiating with a separate consultant who has told them that Cpk will not work in conjunction with GD&T. This is what prompted my first post. I have reviewed the paper and feel that it will adequately describe the process capability. The problem is that I shared teh paper with our contractor who in turn shared it with their consultant. His response was, "Interesting concept but their is no way this can provide a normal distribution." As far as I can tell from all of my research, the distribution must be normal for Cpk to mean anything. I have also gathered that there is a test for normality. My concern is if this paper is adequate it will save the government and the contractor a lot of money. On the other hand, is the consultant unscrupulus enough to discount the paper for the intended purpose of getting business. If this method is valid his services will not be needed. I hope this makes sense. My gut feeling is make some measurements, get some numbers and do a normality check. Is this possible? Any advice on how to do a normality check?

There's actually been a LOT of material written in the Cove about the topic of the application of Cpk's to processes - normal and non-normal. I believe, in a nutshell, there are two broad areas to investigate: the use of PPM(non-parametric approach) or using an approximation to Cpk based on how "non-normal" your distribution is. Regarding the second approach, your Cpk can be fairly accurate even if the distribution is non-normal. The robustness of your Cpk depends on how "robust" the standard deviation is and that depends, in part, on the type of distribution your process follows. A good SPC book (Grant and Leavenworth, Wheeler, etc) would help. Generally, though, the more "tailed" your distribution is, the more problems are created for Cpk calculations. You should search the old forum for Cpk discussions because I'm sure that this has been covered before. Also, a while back, Bert Gunter put together an excellent series of articles in Quality Progress (when he was still writing for the "Statistics Corner") on Cpk applications. Try calling the ASQ and seeing if they can give you a transcript or, if I still have them, I can fax them to you.

Good answer, Roger, thanks.

Tim,

Try these for now and I will have more over the weekend.

Regards,
Don

http://Elsmar.com/ubb/Forum10/HTML/000025.html

http://Elsmar.com/ubb/Forum10/HTML/000024.html

http://Elsmar.com/ubb/Forum10/HTML/000015.html

"Interesting concept but there is no way this can provide a normal distribution."

What I find interesting is that someone would say this without either data nor prior experience to support this statement. I usually view this as a ‘warning’ sign that either the person’s mind is already made up or they are not trained in statistical techniques.

Either way, I would view this comment as suspect. As Roger well stated, it is not necessarily normality that matters, but how strictly you wish to follow the ‘rules.’ Those that have read my posts know I have bent and broken more that I have followed, with somewhat of success (although I view myself as rather less that ‘expert’).

BTW, the test for normality is a Skewness test. If the data are not normal, there are ways to ‘convert’ it to normal. Too detailed to go into here, but any good statistical test will give the procedure.

<FONT COLOR="RED"><BLOCKQUOTE>The contractor has been negotiating with a separate consultant who has told them that Cpk will not work in conjunction with GD&T.</BLOCKQUOTE></FONT></P>

Wrong! Wrong! Find another consultant (would I do :) )

<FONT COLOR="BLUE"><BLOCKQUOTE>As far as I can tell from all of my research, the distribution must be normal for Cpk to mean anything.</BLOCKQUOTE></FONT></P>

No, it must not. It should be, but as I stated above, the normality depends upon how far you are willing to stretch the rules. And, if you are getting Cpk from a control chart (which you could do in the case of MMC), the law of subgroups would apply. This states that regardless of the population distribution, the subgroup sample data would reasonably simulate a normal (see the links above).

The one fixed rule for Cpk is that the process must be in a state of statistical control.

My advice: ditch this consultant and find one trained in advanced statistical techniques, or one that has at least read Grant and Leavenworth.

Ask your questions here. I will help as best I can. If your data are available, e-mail them and I will also help as best I can.

Good luck.

Regards,
Don

May I heartily agree with Don, throw out that consultant.

As I recall, the MMC Cpk paper is how to calculate Cpk based on the allowable bonuses. How can that restrict a process from being normally distributed or not?

How can that restrict a process from being normally distributed or not?

I thank you Batman for your support. I had thought my ramblings had been of a negative nature, which had been the intent. I was absolutely upset that someone would presume this much.

Any process, regardless of the origin and/or source, will either become normal over a continuous period of time or the source of non-normality will sought out and corrected. For anyone to presume that this is not so is either non-enlightened or cares not to be.

http://Elsmar.com/gif/druid.gif

Don and Batman,

Thanks for the vote of confidence. I have given this a lot of thought over the weekend and come to the conclusion that this consultant has a method to sell. The paper I received and forwarded basically cuts him out of a contract. I believe his business half of the brain overrode his judgement. I'll get some data and do some tests.

Thanks Again,
Tim

Does anyone remember anything about the paper? Did anyone ever get a copy? I've also been unsuccessful in attempting to contact Don. The pictures of the wizards he placed in many of his posts were links to his web site - and they're broken so Don might have gone the way of the winds.

*************************************

From: "Jackson, Paul (P.F.)"
To: "'timothy.floyd robins.af.mil'"
Date: Wed, 3 Jan 2001 14:36:43 -0500

Tim, Lassitude, or Kevin,

Each of you requested the paper mentioned below from Don Winton. If you still have it could you share it with me?
Thanks,

Paul F. Jackson
Product Engineer, GDT Strategy (734) 45-80414
ATEO CAD Cube-E234A Ford

> -----Original Message-----
> From: Jackson, Paul (P.F.)
> Sent: Wednesday, January 03, 2001 2:18 PM
> Subject:
>
> Don,
>
> I e-mailed you a month ago or so about the note that you posted on the
> Cove Forum about a paper that you have.
>
> I have found the paper that demonstrates the Cpk calculation for MMC. I
> admit I find it interesting. The paper is in PowerPoint 4.0 and I can
> forward to anyone who is interested.
>
> Regards,
> Don
>
> I have discovered a solution to the problem as well. It will be published
> in Quality magazine in February 2001. The only references that I have
> discovered in my searches of related works are the one that you have
> indicated and another that mentioned an article by "Glen Gruner."
>
> Naturally I am curious to see if the solutions are similar. Could you
> forward me a copy of the article or, if it is unavailable, describe the
> solution.
>
>
> Paul F. Jackson
> Product Engineer, GDT Strategy (734) 45-80414
> ATEO CAD Cube-E234A Ford

Marc,

His website is still up although I do not believe it has been updated recently.

I checked the site and its counter is 'expired' over a year, I think. And I did send mail to that address. We'll see. People do disappear.

Thanks for looking for Don Winton for me guys. Kevin Mader and Timothy Floyd both sent me the Powerpoint Presentation.

What's the name of the file? I'm wondering if I ever got it.

The file is named "Mmc_cpk2.ppt"

Since there are so many request for this paper I think it should be posted on the FTP site.

Not sure if this was ever posted as an attachment or not.

I'm new to this thread so forgive me if I stir up trouble, but I feel I have to comment as I have run into this before, (a true position or GDT spec identified as critical, and therefore our procedures required a Cpk calculation).

I believe GDT was a way to help improve design intent, but also allow for manufacturing to have some more room to vary if they went above the least material condition, (in the case of a hole position for example). It would be a good way to analyze whether or not a specific part was good or bad, if you were sorting for example, but I think you can get yourself into trouble if you try to apply process capability statistics to a GDT dimension.

The question becomes whether or not you could do it, or is there a way to do it, but should you do it in the first place?
Calculating a Cpk implies someone is concerned about process capability,
which implies there is a Cpk level we would like to attain,
which implies a low Cpk should prompt action,
which implies we may want to monitor our process using SPC, so that a negative trend will indicate a preventive measure our operator could take to prevent a problem.

So with our hole true position example, I think the method using % of tolerance is valid, but what does it mean to our operator if the Cpk is low? What process control are we monitoring? Is it the –X- or –Y- position that is varying? If the true position is out, you don’t know what to fix until you look at the readings that went into calculating the true position.

So what I recommend is use to GDT to sort exepensive questionalble product, but ask for a tightened tolerance on an –X- and –Y- position for monitoring process capability.

Andy

Don, can you please forward me a copy of this paper? Deuce, you can download this 'powerpoint paper' from the attachment in Marc's post above.

The % of tolerance method of predicting process capability with the variable "bonus" tolerance does not yield good predictions because the variability of the inputs (bonus tolerance due to feature size) and (feature position deviation) can either be moderated or amplified in the computed variable (% of tolerance). A feature with a large bonus and a large position deviation can have the same value for (% of tolerance) as one that has a small bonus and small position deviation.

The problem is that the variability of the inputs is not always reflected in the variability of the resultant (% of tolerance). I'm think that I have stated this before in other threads but all of the methods that use the variables (bonus tolerance due to feature size) & (feature position deviation) to produce a surrogate variable with a constant USL have similar problems (Glen Gruner's "Adjusted TP", My own "Residual Tolerance", Marty Ambrose's "% of Tolerance").

If one were to plot the distribution "position deviation" on a graph starting with the boundary "zero" and the specified USL @ MMC (I call it the minimum variable limit) and then plot the distribution for feature size on the same graph with its LSL or USL (depending on what size of a hole or shaft produces the minimum bonus) beginning at the positions USL @ MMC you would see two distributions that intersect. The area under that intersection is the probability of a deviation with a variable position tolerance.

If both distributions were normal the Cpu for position would be ((USL[tp]+MEAN[bonus]-MEAN[tp devation])/(3*sqrt(variance[bonus]+variance[tp deviation]))). Unfortunately both distributions are not usually normal but even so the prediction yielded by this equation is typically very close to the predicted results one would get from an attribute gauge (Hard gage). The current practice of ignoring the bonus in a Cpu equation almost never correlates with the attribute prediction. If one were to figure the area under the intersecting curves with a monte-carlo analysis the error could be minimized.

Andy Nutt is correct that it is critical to monitor and control the individual X and Y in a process rather than the computed tp deviation. One can't tell if a mean-shift in X or Y will reduce the tp deviation unless they are the variables being monitored. It is not good however to try to measure the capability of the process by putting upper and lower specs on those coordinate variables.

With variable tolerances processes can be optimized by moving the means of the tp coordinates on target and targeting feature size so that its Cpu equals that of the Cpu for tp deviation.

That's all I have to say for now.