# How to calculate Cpk on Perpendicularity (Cyl Tol Zone at MMC)

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#### Blueplanet

Hello all

I am new and hoping that someone could help me. I am not familair with Cpk yet I am doing a capability study on perpendicularity. i know this is a one sided tolerance but the issue I am having is how do I incorporate a Maximum Material Condition (MMC)? My print spec is .015MM MMC.

The perpendicularity is reletive to a bore; at MMC my highest allowable Perp reading could be .035MM. I am not sure how to plot this; I am using SPC 4 Excel. Would I use .015 as my lower limit and .035 as the high? I would like to know if I am doing this the proper way. For a one sided Tolerance I think I would want to look at Cpu rather than Cpk? Any help would be highly appreciated.

#### Stijloor

Staff member
Super Moderator
A Quick Bump!

Can someone help with this?

Thank you very much!

Stijloor.

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#### ProProcess

I'm not 100% on this myself, but...
The lower limit is going to be 0.0
I see two ways on the upper, and I'm not sure myself.
It could either be the be the .015 and the bonus be applied to the end result.
Or, the bonus would be applied to the upper limit on a part by part basis.
Either way, the upper limit is going to be unique for each part.
I will be interested to see how this thread plays out too!

#### bobdoering

Trusted
My first question is, is this need to calculate Cpk from an automotive customer request? If so, I would lead them to PPAP 4th edition, section 2.2.11.5 where they state the index is not applicable. For non-automotive, you will be fighting Cpk rubber stampers.

The lower limit is going to be 0.0
No, you can not do that. Software assumes that if the lower limit is 0 that the target is half way between 0 and the maximum. That is incorrect, the target is 0. Most software will ask you to omit a LSL in this case, and will report Cpu.

The problem with Cpu is that is answers a different question than Cpk. Cpk is an extension of Cp. Cp tells you how much of your specification is used up by your variation. Cpk answers the question if the variation is centered - based on the assumption that centered is "better", and that the process has a "center" as a target. Cpu has nothing to do with centering (there is no center) and answers the question how far the mean is from the tolerance. Since Cpks are rubber stamped as a requirement to ensure the variation is centered, and Cpu has nothing to offer that question, it is apples and oranges. But, most customers have no idea about this....none. They just rubber stamp. To go through all the gyrations of calculating a Cpk on a GD&T like this is probably a bigger waste of time than most.

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#### Blueplanet

Yes, this is for an automotive customer. The bore related to the Perp. is a two sided tolerance which by the calculations is capable (1.38). My confusion is how would I calculate Cpk for the perp. since each measurement is unique or is my customer asking for something that is not possible? All of the measurments fall withing the print under MMC.

"To go through all the gyrations of calculating a Cpk on a GD&T like this is probably a bigger waste of time than most".

I agree 100%. The problem that I face is that I have to submit a Cpk graph to the customer to prove the process is capable based on a 30 pc sample. If it is not we are required to 100% inspect the features that are not capable. I am new to the company I work for and noticed that what they have been doing in the past was not right. I found this out because they were doing Cpk for flatness. We had a high tolerance of .0007", our measurements were 0 - .0001 but we were not capable. My subordiant was trying to calculate this using a two side tol.

#### bobdoering

Trusted
Yes, this is for an automotive customer. The bore related to the Perp. is a two sided tolerance which by the calculations is capable (1.38). My confusion is how would I calculate Cpk for the perp. since each measurement is unique or is my customer asking for something that is not possible? All of the measurements fall within the print under MMC.
The perp itself is one-sided, isn't it? If so, PPAP 4th edition, section 2.2.11.5 explains that Cpk is not applicable. But, if you bring that to their attention that paints you into a corner, in that it is the only "out" they give you to not do 100% inspection. If you BS their BS requirement with BS data, you might be able to move to a sane sampling plan. It is a mess.

I found this out because they were doing Cpk for flatness. We had a high tolerance of .0007", our measurements were 0 - .0001 but we were not capable. My subordinate was trying to calculate this using a two side tol.
Do not use 0 as a LSL. Leave it blank, calculate Cpu. Better yet, use curve fitting (such as Distribution Analyzer or Minitab) to use the correct distribution to determine capability It will likely show it more capable then using the wrong distribution. If you upload a dataset, I can show you what I mean.

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#### Blueplanet

I am currently looking into Minitab (which I have never used before). Below is the data set.

0.01290.01990.01410.01520.02090.02440.02220.02420.02440.01370.02290.01880.01040.01460.01960.02100.02270.01340.01870.02150.02400.02300.01210.00980.02430.02360.02150.01810.01180.0124

#### bobdoering

Trusted
Here is the results I got off of running through Minitab real quick. Also I attached an Excel sheet for those that want to play with the data.

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#### Paul F. Jackson

##### Quite Involved in Discussions
Blueplanet,

The capability cannot be determined on the (variable limit unilateral tolerance) "0.015(M)" unless you provide the source of that variable tolerance?

Please remit the size measurements and their specified limits associated with the diameter perpendicularity deviations you already provided... see table attached.

Paul

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