# CPK for positional tolerance

Discussion in 'Capability - Process, Machine, Gage …' started by Emil Hortea, Oct 13, 2015.

1. ### Emil HorteaMember

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Hello,

Customer is looking for a cpk on a measurement for positional tolerance of a hole.

The problem I have with this is the nominal measurement is 0 and tolerance is 0.25 but it's a position tolerance, it's not +/- 0.25 (I can't measure negative position).
Does anyone know how to make this or should I make 2 cpk's, one for each axis?

Reports come from a CMM and if I have to make two I would like to know if anyone knows the formula for calculating the tolerance for each axis. Example (Y - Nominal=3, measured=2.976/Z - Nominal=1, measured=1.014 / position=0.055).
I can't find a formula to make this work, should I just try various tolerances until both me and my customer is satisfied (I'm joking here).

Emil

2. ### MinerModeratorStaff Member

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You have several problems here. Cp/Cpk is based on several assumptions, the most critical of which is that the data are normally distributed.

In the position scenario, a hole center could deviate +/- from the target location in any direction. However, the Position tolerance uses an absolute value resulting in a decidedly skewed distribution (probably a folded Normal distribution). This violates the critical assumption of normality making a Cp/Cpk value meaningless.

Your other idea of calculating a Cp/Cpk for the separated X/Y coordinates would resolve the normality issue because the +/- X/Y locations are often Normally distributed, but introduces another problem. You now have a SQUARE tolerance zone instead of a CIRCULAR zone. This means that your Cp/Cpk would be overstated.

And what about bonus tolerances? There are several approaches to dealing with this, but no standard agreement, and each approach gives quite different results.

Need I continue?

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3. ### EmmydMember

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There is a formula that you can use to calculate your true position. We use the sum of squares formula. It works for both 2D & 3D true positions. I've attached a file that you can use. Hope this helps!

#### Attached File(s): 1. Scan for viruses before using. 2. Report any 'bad' files by reporting this post. 3. Use at your own Risk.:

• ###### True Position Calculator.xlsx
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4. ### Emil HorteaMember

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Thank you Emmyd for the calculator, at least now I understand the formula but I fear Miner is correct, I can't to a Cpk on position.
I just hope customer will understand and be satisfied with GR&R, we managed to get 6.01%!

Cheers,
Emil

5. ### Bev DModeratorStaff Member

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Emil - most customers that have positional tolerances are looking for the vector approach to the two (or 3) axes. mathematically this solves the square problem you get by trying to calculate an index for each axis. Emmyd's spreadsheet is correct for that application.

However, now you have the 'one sided', non-normal distribution problem that 'modern thinking' on capability indices abhors. AIAG does have an out for this:

AIAG PPAP 4th Edition, 2.2.11.5 Processes with One-Sided Specifications or Non-Normal Distributions:

NOTE: The above mentioned acceptance criteria (2.2.11.3) assume normality and a two-sided specification (target in the center).
When this is not true, using this analysis may result in unreliable information.
…These alternate acceptance criteria could require different type of index...
(Many thanks to Bob Doering for continually pointing this out)

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6. ### ncwalkerWell-Known Member

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The only way I have ever done it that sat with me well was to calculate a principal variation. (Think principal stress). Basically, in order to get position you do have an "x" and "y" measurement. With no guarantee that your maximum noise will be aligned with either x or y. So you take the standard deviation of the x's and the standard deviation of the y's and calculate the square root of the sum of the squares to get the "principal" standard deviation. Think the hypotenuse of a right triangle. This is the maximum variation. Your tolerance is then your positional tolerance and you use this worst case standard deviation in a regular Cp/Cpk calculation. As others have said, this doesn't account for bonus tolerance. To do that, one could just use the RFS tolerance (because if THAT is capable, it would be capable with the bonus tolerance). OR you could increase the bonus by an average bonus tolerance. Again - it's not well defined....

7. ### EmmydMember

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We have also done Cpk on bonus tolerances by reporting this true position as a percent of allowed tolerance. Say your position was 0.5(MMC) A B(MMC) C(MMC). Total tolerance allowed would be 2 and your actual position using the sum of square formula was 1. You used 50% of your allowed tolerance, and this percentage is what you would enter into your Cpk calculator. That has been the only way I've found to accurately reflect a positional callout when bonuses are allowed.

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