Cpk for Unilateral Tolerance

OmarEn

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#1
Hi Guys,

I have three situations trying to do a Cpk with unilateral tolerance. I hope you guys can give me some advice on this.

1. I want to conduct a CPK for a diameter that is 10.0mm +0.1 -0.0

2. I want to conduct a CPK for a diameter that is 10.0mm minimum (it does not have a maximum limit).

3. I want to conduct a CPK for a flatness of 0.3mm.
As you may know, flatness tolerance is an absolute value. It means that the spec is maximum 0.3mm since there is not a possibility to have a value less than 0 since 0 would be a perfect flatness.

I am trying to complete this in Minitab but I do not know if it is possible to calculate ability for processes with this kind of tolerance.

thanks in advance for your time.
 
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OmarEn

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#3
Hello Marc,

Yes, I had been looking for andwers in another existing discution. But my questions are a bit different.
 

Marc

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Staff member
Admin
#4
Hopefully someone here will help in the next day or two. GD&T isn't in my specialty domain.
 

Miner

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Staff member
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#5
Hi Guys,

I have three situations trying to do a Cpk with unilateral tolerance. I hope you guys can give me some advice on this.

1. I want to conduct a CPK for a diameter that is 10.0mm +0.1 -0.0
In Minitab, enter 10.0 and 10.1 as the spec limits. Under Options, enter 10.0 as the Target. Cpk will be calculated using the 10.05 as the center of the spec, but Cpm will be added to the output and will use 10.0 as the target.

2. I want to conduct a CPK for a diameter that is 10.0mm minimum (it does not have a maximum limit).
Enter 10.0 as the Lower spec and leave the upper spec field blank.

3. I want to conduct a CPK for a flatness of 0.3mm.
As you may know, flatness tolerance is an absolute value. It means that the spec is maximum 0.3mm since there is not a possibility to have a value less than 0 since 0 would be a perfect flatness.

I am trying to complete this in Minitab but I do not know if it is possible to calculate ability for processes with this kind of tolerance.
Enter 0 as the Lower spec and check the box labeled Boundary. this tells Minitab that it is not possible to have values below zero. Enter 0.3 as the Upper spec.
 
Last edited:

bobdoering

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#6
First, note that AIAG PPAP 4th edition 2.2.11.5 (NOTE) states that Cpk and Ppk "assume normality and a two sided specification (target in the center). When this is not true, using this analysis may result in unreliable information."

I can attest that the statement is a fact. I can also attest that MANY people that request Cpk's have never read it and simply rubber stamp the requirement with zero statistical knowledge.

That being said...

1. I want to conduct a CPK for a diameter that is 10.0mm +0.1 -0.0.
Cpk does not care how the dimension is called out, it cares about the distribution and the distance of its mean to the closest specification. If the process variation is independent, random and normal, calculate Cpk with the 10.0 mm to 10.1 mm specification.

2. I want to conduct a CPK for a diameter that is 10.0mm minimum (it does not have a maximum limit).
If the process variation is independent, random and normal, simply calculate CpL. The distance to the specification is what you need to know.


3. I want to conduct a CPK for a flatness of 0.3mm.
Unless you have poor flatness control (very far away from 0) you have a non-normal distribution. See note above.

Rather than rehash the whole thing here on this example, check out this blog on the topic:
https://elsmar.com/Forums/blogs/bobdoering/309-unilateral-tolerance-capability-calculation.html
 
#7
Minitab can definitely handle all of those calculations. As a note, some distinguish Case 1 as an "asymmetric" tolerance and Cases 2 and 3 as truly "unilateral."

Case 1 often appears in machining especially where fits and clearances are concerned. As such, the nominal dimension is just a convention. Example: a pin is specced as diameter 10 -0.05 / -0.10 and a hole as 10 +0.1 / -0. The nominal 10 serves as a common reference point.

In cases 2 and 3, there is effectively no Cp index - only Cpk. More specifically, for a minimum spec (no max such as Case 2) there is only CpL. Likewise for Case 3 there is only CpU.

There is one slight difference - Case 3 has a theoretical boundary at 0 which can affect the results. Minitab has an option to specify a limit as a boundary which should be enabled in this case.

On a final note, some situations do occur where specifications such as 10 +0.1 / -0 actually convey a target (ideal) of 10 instead of the usual "halfway between the limits" interpretation. An example might be an assembly where the goal is "flush," but being slightly proud has more consequences (damage, interference) than being recessed (annoying). A good FMEA can help identify such cases. The CpM index takes the "target" into account and is especially relevant for those kinds of scenarios.
 

OmarEn

Involved In Discussions
#8
Wow, your answer guys are really helpful... All of them.
Now I have a more clear idea of how to deal with this.

Thanks a lot.
 
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