# Thread: Philosophy of Determining CPK for a flatness tolerance.

1. ## Philosophy of Determining CPK for a flatness tolerance.

I have a molded component contains a surface of ~ 50 x 50 mm which has a flatness tolerance of 0.5 mm.

The part is being measured on the CMM and all I get from the CMM report is a value for the flatness between 0 and 0.5 for each part measured.

The dimension is critical so we are expected to calculate CPK.

I can not get my company, the end Customer, or myself to agree upon a satisfactory method to do so.

- My company feels that we should take the value reported by the CMM on 100 parts and calculate the CPK. My concern with this is that the CMM is only giving me a value and this value can be anywhere on the 50 x 50 surface for each given part so I am not sure I am getting a meaningful CPK result (makes me feel like I am taking the average of some averages and trying to prove something with it).
- My Customer feels that we should only be calculating the capability of each part individually - that is looking at the 25 points, or whatever, the CMM is taking on the 50 x 50 surface and calculating CPK for each part. I am not sure how this gives me process capability it will only give me 100 CPK numbers. I also don't see how this gives me process capability.
- My thought is that to show capability I need focus on 4 or 5 points on the 50 x 50 surface and calculate the capability across the 100 pieces at the exact same points generating 4 or 5 CPK numbers.

Any more thought?

2. Flatness on molded parts is an almost impossibility to asses due to the the many variables associated with the cooling and setting process.

Also flatness of one side may be affected by the other side. How are you supporting the part to be measured on a single-side?

Once points are gathered by whatever means, I think you are going to require some statistical analysis software to arrive at a QC-usable figure to test for flatness of incoming production parts.

This quest falls closely aligned with the knapsack theory and people have spent lifetimes trying to resolve those conundrums.

3. Being able to assess and being able to meet are two different things. Obtaining flatness on a molded part is difficult to meet but assessing how poorly you made the part is feasible.

The part clamped to a fixture to it's functional datums on the CMM. The datums are not on or near this surface.

Assuming there is nothing incorrect about the measurement method (which for me is a different conversation) I would hope that the philosophy of how to calculate capability would be less complex than the knapsack theory.

I think my question extends beyond flatness so let me reformulate my question a bit. I have a flange on the end of a pipe which has a groove to hold an o-ring which forms a face seal with the adjoining piece of pipe. The depth of the groove is controlled to the face of the flange by a basic 5 and a profile back to the face of 1. So essentially this groove depth is 5 +/- 0.5 mm. I inspect it with a gage that sits on the face of the flange and has 24 holes which allows me to insert a depth mic and contact the groove. From these 24 measurements I am given the worse case measurement as the result for profile. There is no guarantee that this worse case result happens at the same place on every piece manufactured.

1. Is it proper to run capability on the profile number given for the entire groove on 100 samples.
or
2. Is it proper to run capability on the 24 points for the single groove?
or
3. Is it proper to run capability on all 24 points individually across the 100 samples giving me 24 CPK numbers?
or
4. All three.
or
5. Something complete different.

Basically what is the proper method to feel confident that the 1.67 CPK we are getting truly represents that we have a capable process.

4. Originally Posted by blakev
I have a flange on the end of a pipe which has a groove to hold an o-ring which forms a face seal with the adjoining piece of pipe. The depth of the groove is controlled to the face of the flange by a basic 5 and a profile back to the face of 1.
Well, given that piece information, the flatness to a large degree becomes moot? Isn't the ability of the o-ring take up gaps more important? Providing the best and worst case gaps are covered well by the o-ring, then a high degree of flatness measurement would seem to me to be somewhat unimportant, even academic. Providing a relatively close/accurate measurement can be made and the parts produced within that scope, then surely that should suffice.

If there were no o-ring then I could get involved with the need for greater flatness measurements but at this point I feel you are all arguing over a theory. Probably my best guess would be the first option (your Boss', not just because he is the Boss) but I would take an RMS value over the 100-parts and call it a day. Because your CMM can measure to millionths, it is not to say that it has to. It's the job of the o-ring to make the seal.

Just one old fart's thoughts on it. You may want to check the current bearing/pulley drama thread unfolding here on the rampant over-use (my opinion) of tolerances. Parts defined to 3-Metric decimal points.

5. My view is that when you're requested to present a Cpk for flatness, it's meant for a spread of many parts, not just the points measured on one part. When checking one part for flatness with a CMM, we have to be careful. If I sample three points on that surface, it will be perfectly flat! If I check 10 points, it is better. But if I check 10,000 points on that surface, we are getting a better feel for the correct flatness error.
So I don't think you should apply the Cpk idea to one part's flatness measurement; the number of points measured doesn't change the flatness error, it just changes the confidence you have in your reading.
The Cpk should be checked over a spread of 100 (or whatever) parts, so my vote goes to your company, not your customer.

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