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

B

Blueplanet

#11
Paul

Here is the diameter data. The tolerance on the diameter is +/- .010mm

49.0045​
49.0092​
49.0071​
49.0092​
49.0072​
49.0092​
49.0097​
49.0086​
49.0092​
49.0045​
49.0063​
49.0097​
49.0086​
49.0065​
49.0053​
49.0071​
49.0086​
49.0063​
49.0053​
49.0041​
49.0056​
49.0089​
49.0086​
49.0041​
49.0092​
49.0041​
49.0056​
49.0063​
49.0072​
49.0038​
 
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Paul F. Jackson

Quite Involved in Discussions
#12
Blueplanet,
Attached is your data for Ø perpendicularity and hole size added to the spreadsheet PpkMMC.xls from the reference Cove discussion threads that are suggested below.

To summarize you have a hole diameter tolerance of ??.?? ±0.01 (I assumed 49.00 ±0.01) and you have a variable limit tolerance 0.015(M) that is 0.015 when the hole diameter is 48.99 and 0.035 when the hole diameter is 49.01.

When viewing the histograms of both the size and geometric deviation I see both distributions are skewed toward an upper boundary (as if) the parts have been sorted for occurrences above those boundaries or something in process limits them. Let me say that the spreadsheet for predicting conformance of this variable limit tolerance assumes both distributions are normal and that the data generating them is random (in-control) which does not appear so... never-the-less it should closely correlate with the results achieved with an attribute "GO" gage.

The spreadsheet results of the process "as is" predicts a Ppk for size (assuming its tolerance is 49.00 ±0.01) is 0.51 and perpendicularity MMC is 0.85.

The spreadsheet suggests that the process potential Pp for both simultaneously is 0.76 if the mean hole size was adjusted downward 0.0015 reducing the hole size distribution's encroachment in its USL.

Paul
 

Attachments

Paul F. Jackson

Quite Involved in Discussions
#13
Maybe I should say something about how the spreadsheet is designed.
It acknowledges that the variable limit tolerance is derived from the feature's size which is itself a distribution. Since the tolerance is a distribution it cannot be expressed as a constant limit like all other capability prediction models.

Since the minimum amount of your variable tolerance is 0.015(@MMC) and it corresponds to the hole's MMC size of Ø48.99 and the maximum amount is 0.035(@LMC) corresponding with the LMC size of Ø49.01... we can plot the histograms of the two distributions adjacent to each other to see if they intersect. The intersection of those two distributions represents the probability of a defect for the variable limit position tolerance just as the intersection of the size distribution with its USL 49.01 reveals the probability of the size being too large.

Interestingly... if one were to make an attribute gage to check this tolerance the pin size would be set to 48.99-0.015=48.975 which is called the "virtual condition boundary" of the variable limit tolerance. You can see on the graph that the size 48.975 corresponds with a 0.0 perpendicularity tolerance, 48.99 corresponds with the minimum specified perpendicularity tolerance 0.015, and 49.01 corresponds with the maximum 0.035 tolerance.

The equations used to predict the probability of the intersection of the two distributions are given in the instructions and the optimization or Pp (process potential capability) is predicted by recommending the optimum feature size adjustment to minimize the probability of a defect for both specifications simultaneously (specifically each distribution's encroachment on its upper limit).

Paul
 
B

Blueplanet

#14
Paul

I am sorry; I did not realize that I did not post the nomial for the diameter. The nominal size for the diameter is 49.005 +/-.010. Low limit is 48.995 and upper limit 49.015. I entered the proper USL and LSL and have a PPk of 1.36. Were you able to make that graph in Excel exclusivly or is that the by product of an add in software? I am currently looking into Minitab for SPC analysis.

Thanks for your help:agree1:
 

Paul F. Jackson

Quite Involved in Discussions
#15
You cannot do this in Minitab unless you can write your own script to examine intersecting distributions. I just used excel.

Without considering any variable tolerance "RFS" your Ppk for pperpendicularity is estimated at -0.24, and size 1.36, with the variable tolerance considered it is 0.51 for perpendicularity and 1.36 for size. If the mean size was adjusted to its optimum target the potential capability for both simultaneously would be maximized at 0.76.

Paul
 

Attachments

Last edited:

Bev D

Heretical Statistician
Staff member
Super Moderator
#16
<rant on>
:soap:This is my professional opinion and personal advice.

First let me disclose that I am viscerally opposed to capability indexes. I feel that to describe variation in terms of a single number is not only an oxymoron but a non-value-add requirement. Why on earth would I want to essentially throw away all of that data to concentrate only on the final resulting index?

We want to understand our process capability for two reasons: to predict yields (& field failure rates) and to understand the variation in the case of stackup tolerances and wear failure modes (especially when tolerances cannot be precisely engineered).

Industry desires to use these numbers to know if we can reduce inspection from 100%, understand potential impacts to delivery and availability, cost ramifications of rework or safety stock, protential escape to teh customer's line and or the end user, effect on reliability,etc.

The common indices are based on an assumption of Normality. The Normal distribtuion near and beyond +3 sigma is very susceptable to large inaccuracies even when the distribution is symmetrically bell shaped. Thsi results in very misleadign information for both reasons for a process capability study.

Additionally, many of features, dimensions and functions are not clear cut double sided tolerances. This results in our doing 'extra' math work to come up with that single number...and GD&T makes this even more complex.

So is this work non-value-add? unfortunately, too often our Customers are inundated wiht indices and to save tiem they only check to see if the number is greater than the required level. they check the box...after all this work is done ask yourself: what have I learned? what has my Customer learned? How will my products be made better by this analysis? Is there a better analysis that woudl be even more effective? Do I have time to do that after calculating a bunch of Cpk values?

These issues are even more destructive when it comes to 'bonus' tolerances. Remember that bonuses tolerances are benefit of a lack of variation reduction of the feature or dimension to the target specifications. You get to 'take advantage' of this extra variation.

In reality if we are concerned about REDUCING PROCESS VARIATION, the index should be calculated based only on the native variation to the specified tolerance without any bonus. If we are only interested the YIELD, then a simple defect rate using the bonus tolerance (back calculated to a Cpk if you must) should be sufficient. If I were pushed to submit a single number in yoru case I would choose this latter option. It's quick and easy. Then you might have some time to work on really understanding your process capability.

The only thing 'wrong' with plotting our data in time sequence against the specification limits so we can see all of the components of variation (within piece, piece to piece, lot to lot, raw material lot to lot, time to time, etc.) is that we must engage our brains and THINK about our data collection strategy and then think about the resulting plot. So to avoid this we spend our time on figuring out how to check the box...

But I readily admit that my position on this is a bit like emptying chamber pots into the incoming tide. Society - and industry is just a microcosm of society - is just too enamored of the quick fix, simple explanation, great sounding sound bite...

<rant off>
 
B

Blueplanet

#17
Bev

Thank you for your advice. When I posted this question I assumed that this would be a cut and dry answer. I have not done stat's or math of this level in a long time. I am having trouble comprehending what is going on. My diameters are capable and I am given a "bonus" for my Perp tolerance; which none of the measurements exceed the tolerance. The parts are all manufactured on the same CNC machine, same tooling, and same fixtures. I think more than anything the variation is coming from the CMM. I agree with what you are saying but in the end I have to provide a piece of paper to the customer that says my process is capable. According to what Paul's calculations/ graphs are showing me; my process is not capable.
 

Paul F. Jackson

Quite Involved in Discussions
#18
Bev,
I sympathize with your angst concerning the one value that so many are demanded to deliver to continue doing business. At the same time however I applaud Blueplanet's question and his seeking to understand how this one value can be addressed in this tolerance situation.
You said,
"These issues are even more destructive when it comes to 'bonus' tolerances. Remember that bonuses tolerances are benefit of a lack of variation reduction of the feature or dimension to the target specifications. You get to 'take advantage' of this extra variation.

In reality if we are concerned about REDUCING PROCESS VARIATION, the index should be calculated based only on the native variation to the specified tolerance without any bonus."
What would you say if his specification was written,
Ø49.015
Ø48.980 [Perpendicular|Ø0.0(M)|A]
rather than,
Ø49.015
Ø48.995 [Perpendicular|Ø0.015(M)|A]
as a specifications where the geometric tolerance is totally variable (dependent upon feature size) acknowledging that the part will functionally assemble even when it does not conform to the chosen proportions for size and the geometric control. Indeed the former is prohibited because there is no statistical vehicle (other than an attribute prediction) to measure its predicted conformance against the one value.

I disagree with you about the role of "bonus tolerance" that I prefer to call variable limit tolerance. It is defined the way it is because it is the way the real parts work and assemble. Is it improperly applied to designs? Absolutely!!! Is it summarily ignored in continuous data statistical conformance predictions? Absolutely!!! Should we continue to ignore it for those reasons? Absolutely not!!!

I think you will agree that the real value is realized in examining the data and improving the process so that the probability of a defect is so remote that the process performance can put statisticians out of business. Is Blueplanet's hole shallow or deep? What is causing such a uniform or skewed distribution for both perpendicularity and size? If the holes are shallow is the perpendicularity deviation generated mostly from measurement error or finish? If it is deep is its orientation deviation predictable... can its mean orientation error be adjusted? Why is the size skewed toward the upper limit? Do we even have enough data to make any valid conclusions???

If all these questions are addressed... what is the best capability that we can expect from this process and consequently what is the target we should set for feature size to achieve it.
Paul
 
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Bev D

Heretical Statistician
Staff member
Super Moderator
#19
I think more than anything the variation is coming from the CMM.
Have you performed an MSA? Have you plotted your data in a time series chart to assess stability and components of variation? These are REAL capability studies that will be much more informative to you at this point - and help you get the right number to your Customer.


I agree with what you are saying but in the end I have to provide a piece of paper to the customer that says my process is capable.
Why can't you just send them a Cpk back calcuated from the defect rate? it's still a Cpk. If your process really ins't capable this will be tough to do. (See above)
 
B

Blueplanet

#20
Bev


I have not done an MSA. The CMM was recently calibrated. I do not like to use the CMM as the gospel but sometimes I have no other choice. I do not like the software we are using. I just had an instance were I had to check form comparing a plane and a diameter to a counter bore. All the dimensions were machined at once. Using the form function in the program the CMM is telling me my form is out .002; which to me is impossible). I set the part up on a jig bore machine and swept the bore with an .0001 indicator and seen .0001 movement. The tolerance max for form is .0005.

I am not sure what you mean by back calculate from the defect rate.
 
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