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

Bev D

Heretical Statistician
Staff member
Super Moderator
#21
Bev

I am not sure what you mean by back calculate from the defect rate.
To 'back calculate' means you take the defect rate, convert it to a Z score then divide by three.

so in excel Cpk = [NORMSDIST(1-p)]/3 where p = defect rate.

the defect rate can be the defect rate using the bonus tolerance...
 
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Bev D

Heretical Statistician
Staff member
Super Moderator
#22
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.
We agree on this. I don't have anything against the use of 'bonus' tolerances to accept and ship parts that will work. that's just good business sense. I am opposed to using for them for statistical analysis (beyond my comment below) and process improvement. Tehre are times when variation reduction is nto cost effective due to technology and organizational maturity issues. However, often we can reduce the variation and then have no need for 'bonus' tolerances...

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!!!
uhhhh. Here is where I have issues. Using statistical capability models which rely on a fairly accurate assumption on the underlying distribution to predict future conformance is seductive, but ultimately futile in my experience. I have found that we are far better off if we understand the process, characterize the inputs and outputs and where applicable create real models of Y=f(X) form to control our processes. If we need to know how many defects we are making a simple counting of the defects we actually encounter is usually close enough for any business purpose and is far easier than distributional models. (I prefer to spend my statistical energy on analytic studies that improve and really predict future performance than to waste energy - and time - on precise enumerative studies of material I've already made and then use that to 'predict' future performance.)


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.
Absolutely. except that I think statisticians are still needed...

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???
All great questions that go to true capability; the Cpk value and it's calculation have no bearing on these questions....but they are the money making questions...
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#24
how many times did you have to invoke the bonus tolerance?

The alternative is to look at the totality of your process and not just some arbitrary 30 piece sample. 30 pieces can be good enough IF they are representative of your process - typically a random sample from some substantially larger population produced over time. Too often I see these capability studies done only on the last 30 sequential pieces or the last 30 samples and they aren't representative.

What is your current defect rate (last 3 months)? Can you plot your results for the last 3 months in time series? (I don't know the volume of your production or your current sample plan so 3 months is a guess...)

I think the barrier you are experiencing right now is your own internal constrained thinking (I don't intend that to be a mean or insulting comment). There are other ways to do this but you need to be open to considering them. What you are hearing from the folks here is that you are running down a dead end alley with your current 30 piece sample approach. We need to get you on a different path to determine capability.
 
B

Blueplanet

#25
We are a job shop. The customer has an order of 300 pcs. Under their requirments we do a capability study on the first 30 parts. The customer picks several features they want the capability study on. We do the study and if our Cpk is > 1.33 then we are not required to perform 100% inspection on the features that meet their Cpk requirements. If we do not then 100% inspection is required along with every measurement documented (which we have to submit with the parts). The customer will field test these parts and then have them manufactured else where. We only have a couple customers with this requirement.
 

Paul F. Jackson

Quite Involved in Discussions
#26
Quote:
Originally Posted by Paul F. Jackson


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!!!
Originally Posted by Bev


uhhhh. Here is where I have issues. Using statistical capability models which rely on a fairly accurate assumption on the underlying distribution to predict future conformance is seductive, but ultimately futile in my experience. I have found that we are far better off if we understand the process, characterize the inputs and outputs and where applicable create real models of Y=f(X) form to control our processes. If we need to know how many defects we are making a simple counting of the defects we actually encounter is usually close enough for any business purpose and is far easier than distributional models. (I prefer to spend my statistical energy on analytic studies that improve and really predict future performance than to waste energy - and time - on precise enumerative studies of material I've already made and then use that to 'predict' future performance.)

I was speaking of the appropriate application and use of the variable MMC or LMC tolerance modifier on the design not the reliability of the distribution model.

If one chooses not to apply the variable tolerance in a continuous data model and the variable portion is ignored then he also chooses to accept economic penalties of rejecting and scraping potentially conforming product.

If a competent continuous data model cannot be then you are left with using the attribute data model and you know how many defect free instances are permitted in many thousands of parts to make a simple prediction from that. One is better off resigning themselves to a 100% attribute gage check.

If it was my process I would pay attention to the details until I understand their behavior over time with continous data until I can demonstrate the processes inherent ability to produce to those specifications... then either strive for improvement or consider an alternate process.

Paul
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#27
We are a job shop. The customer has an order of 300 pcs. Under their requirments we do a capability study on the first 30 parts. The customer picks several features they want the capability study on. We do the study and if our Cpk is > 1.33 then we are not required to perform 100% inspection on the features that meet their Cpk requirements. If we do not then 100% inspection is required along with every measurement documented (which we have to submit with the parts). The customer will field test these parts and then have them manufactured else where. We only have a couple customers with this requirement.
Well the first 30 pieces violates the whole premise of a capability study.
If it were me, then I would simply do a straightforward calculation of the capability without regard to the bonus tolerances. Bonus tolerances should only be applied part by part anyway so if you fail the 'study', 100% inspection is the right thing to do. If you pass you don't need the bonus tolerances.
 
B

Blueplanet

#28
I thought that a capability study could be done using 30 pcs, using 3 sigma instead of 6?

Paul noted that the diameters were on the high side above the nominal; this was not a drift in our process we did this to use the MMC bonus. I was able to do a graph in mini tab under capability analysis using Stat > Quality Tools > Capability Analysis > Normal (assumed). The graph does not show the typical +/ - sigma it just shows the LSL; it does however give me a Cpk of 2.19 for my perp; which I think the customer will buy.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#29
I thought that a capability study could be done using 30 pcs,
30 pieces is on the low side but it is a rough 'rule of thumb' for the minimum number of pieces. If we are serious about the answer, the sample size is dependent on the standard deviation of the process and the amount of accuracy we desire for the estimate of the index, average and SD. 100 samples is a better rule of thumb for a minimum sample size

BUT the SIZE isn't the biggest issue, the randomness of the sample is. Your customer is requiring a bastardized version of a capability study - it is a blatant misuse and misunderstanding of statistics. But you're stuck with their simplicity...My advice is: do the minimum youhave to do to make yoru customer SQE happy and focus your efforts on real quality problems...


using 3 sigma instead of 6?
I have no idea what this means to you. Capability studies for capability index calculations use +/- 3 sigma about the mean
 

Paul F. Jackson

Quite Involved in Discussions
#30
I thought that a capability study could be done using 30 pcs, using 3 sigma instead of 6?

Paul noted that the diameters were on the high side above the nominal; this was not a drift in our process we did this to use the MMC bonus. I was able to do a graph in mini tab under capability analysis using Stat > Quality Tools > Capability Analysis > Normal (assumed). The graph does not show the typical +/ - sigma it just shows the LSL; it does however give me a Cpk of 2.19 for my perp; which I think the customer will buy.
Blueplanet you must use 0.015 as your USL for your capability in Minitab... you cannot add the maximum variable tolerance allotment to your USL to predict conformance. When I figured the RFS capability with your data the Cp(upper) was a negative number meaning that the mean perpendicularity deviation was above the Minimum variable USL 0.015.

Paul
 
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