How to perform Process Capability for true position

QE1993

Involved In Discussions
#1
The nominal for true position is 0. The print will call out a GD&T true position and allow you to go up to, let's say, .003. In cpk software, how do you reconcile this? If we put our LSL as 0 and our USL as .003, we don't get accurate results, because the LSL is NOT 0 - 0 is the nom.

Is there a way to 'obsolete' the LSL and just focus on the USL when it comes to true position?

By the way, I am using Minitab to do my capability studies.
 
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Stijloor

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#2
The nominal for true position is 0. The print will call out a GD&T true position and allow you to go up to, let's say, .003. In cpk software, how do you reconcile this? If we put our LSL as 0 and our USL as .003, we don't get accurate results, because the LSL is NOT 0 - 0 is the nom.

Is there a way to 'obsolete' the LSL and just focus on the USL when it comes to true position?

By the way, I am using Minitab to do my capability studies.
This question has come up a few times.

If you scroll down, you'll find a few interesting threads and responses.
 

Miner

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Staff member
Admin
#5
The nominal for true position is 0. The print will call out a GD&T true position and allow you to go up to, let's say, .003. In cpk software, how do you reconcile this? If we put our LSL as 0 and our USL as .003, we don't get accurate results, because the LSL is NOT 0 - 0 is the nom.

Is there a way to 'obsolete' the LSL and just focus on the USL when it comes to true position?

By the way, I am using Minitab to do my capability studies.
The specific answer that you requested (i.e., 'obsolete' the LSL in Minitab) is straightforward. When you enter 0 as the LSL, check the box labeled 'Boundary'. This tells Minitab that 0 is a physical limit instead of a spec.

However, capability studies for GD&T are rarely straightforward. Since position tolerances convert Cartesian coordinates into partial Polar coordinates, you will often end up with skewed (non-normal) distributions. If you add in MMC modifiers, you no longer have a fixed tolerance either.
 

QE1993

Involved In Discussions
#6
I believe our CMM program accounts for the bonus tolerances due to the MMC modifiers.

Can you please explain a little further what you mean by "Since position tolerances convert Cartesian coordinates into partial Polar coordinates?"

How do you combat this in a cpl study?
 

Miner

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Staff member
Admin
#7
Let's use an example of a square block with a hole drilled into it. For simplicity, I am using only the X & Y coordinates. One corner of the block is the 0, 0 datum, and the hole is drilled at coordinates 1, 1. This is a Cartesian coordinate system. This is the system in which a CMM operates and usually reports data in an x, y, z format.

Therefore, the hole location has an x coordinate and a y coordinate. It may vary less than 1 or greater than one. If you were to analyze the x or the y results individually, chances are good that you would see a normal distribution in each axis.

However, Position results convert the separate x, y coordinates into part of a quasi Polar coordinate system. A true Polar coordinate system would provide both a radial distance and a polar angle for each measurement. Position results consider only the diametrical distance regardless of the angle. Therefore, a hole at (0.9, 0), (1.1, 0), (0, 0.9), or (0, 1.1) are all considered to have the same Position despite the fact that they are off location in four different directions. This usually results in a right skewed distribution.

Not only do you have to either perform a non-normal capability analysis, or transform the data to normal (not recommended), but you do not have the necessary information to improve the capability. To get that information, you have to study the x and y results separately in order to move the hole onto target.
 

Miner

Forum Moderator
Staff member
Admin
#8
I believe our CMM program accounts for the bonus tolerances due to the MMC modifiers.
It does when reporting whether an individual result in in/out of tolerance. However, when you combine 100 of these into a capability study, you end up with 100 different bonus tolerances.
 

QE1993

Involved In Discussions
#9
Thank you for replying to me. I'm afraid I have some more questions, but feel free to ignore them if you don't have the time.

So, I can determine the distribution of my data and then perform the capability study based off of that model?

When you say that I have to study the X and Y coordinates separately, do you mean I should determine the capability of each coordinate individually? Can you help me understand how that would help me improve the overall capability of my process?

I guess all my questions really boil down to, what is the most accurate (if any) cpk results for a GD&T dimension? And how can I obtain those cpk results?
 

Miner

Forum Moderator
Staff member
Admin
#10
So, I can determine the distribution of my data and then perform the capability study based off of that model?
The standard capability study assumes that the process is stable and the distribution of the process is normal. Therefore, you must collect data in time sequence, plot it on a control chart to verify that it is stable, then verify that it is normally distributed. If the process is stable, but is not normally distributed AND there is a rational reason for it to be non-normally distributed, you can perform a non-normal capability analysis (recommended) or you can transform the data into a normal distribution (not recommended).

When you say that I have to study the X and Y coordinates separately, do you mean I should determine the capability of each coordinate individually? Can you help me understand how that would help me improve the overall capability of my process?
Take a scenario where you have a Cp = 2 and a Cpk = 0.8. Obviously, you need to reduce the average Position by moving the feature closer to target, but how? Is the feature off in one axis? Both axes? Do you need to reduce the dimension or increase the dimension? The only way to tell is to evaluate the capability for each axis.
 
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