How to Calculate Cpk with only a Minimum Tolerance

F

FASTENERS

#1
I am pretty new to the capability analysis area and I do need help.

I am working on determining the Cpk for torque values. as an example

(58,60,32,56,29,36) are the values in inch pounds. The spec states that

the torque must be 30 inch pounds minimum.

How do you determine Cpk for a one sided limit that doesn't have a max?


Thanks in advance
 
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bobdoering

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#2
Re: How to calculate cpk with only a min tolerance

I guess the first question is why would you want to? The point of Cpk is to correct Cp values to show whether a distribution is centered within the specification, not just within a specification. You do not need to answer that question, so is this being done as a forced march by a customer? Also, what is the gage R&R of your testing? How much of your variation is from the part versus the testing? I just bring that up because Cpk calculations are of dubious value to begin with, even more so with a unilateral tolerance and further dubious if the testing itself is a significant source of the variation.
 
F

FASTENERS

#3
Re: How to calculate cpk with only a min tolerance

Thanks for the reply. I did explain that to our customer as well. This requirement was listed in one of their specs and that is why i was searching posts for an answer. I wanted to know if there are no set limits upper and lower limit what would the cpk show?
thanks again
 
A

AdamP

#4
Re: How to calculate cpk with only a min tolerance

... determining the Cpk for torque values. as an example

(58,60,32,56,29,36) are the values in inch pounds. The spec states that

the torque must be 30 inch pounds minimum.

How do you determine Cpk for a one sided limit that doesn't have a max?
At its simplest, capability speaks to how well your process variation fits with the customer defined 'tolerance' or specification range. A general story used to explain Cp and Cpk is that Cp addresses whether a car will fit within a garage and Cpk addresses where in the garage the car is located.

So given that - plus the good comments Bob has made, you have a few things to consider for your situation. With a one-sided spec, you have more of a carport than a garage. :) But are being asked to use Cpk to show the fit.

Cpk by formula is = (min( USL - avg, Avg - LSL))/ 3 std dev

In your case you take the Avg - LSL to get your numerator and use 3 standard deviations for the denominator to get the ratio. So you can satisfy the expectation of producing a Cpk value.

A few more issues though: Bob has mentioend the measurement variation, which you'll need to know. Also, with this being torque with a minimum spec of 30, you could over-shoot the torque and (making this part up) have a mean of 60 with a small standard deviation and show a very impressive Cpk. and you could be completely over-tightening. Since we don't know much about what you're tightening, this might not matter, or it could matter with respect to fatigue or other material/stress issues.

One last bit - Cp and Cpk both assume normality of data. While you're running your MSA (Gage R&R), check the distribution of your data and see if it passes a normality test. If not, you may need to propose an alternate capability measure to your customer, should they care about things like that.

Hope this helps,

Adam
 

bobdoering

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#5
Re: How to calculate cpk with only a min tolerance

Thanks for the reply. I did explain that to our customer as well. This requirement was listed in one of their specs and that is why i was searching posts for an answer. I wanted to know if there are no set limits upper and lower limit what would the cpk show?
thanks again
If your customer is automotive, refer them to the PPAP manual 4th edition, section 2.2.11.5 concerning processes with one sided specifications and its associated note that the Cpk index assumes normality and two-sided specification with the target in the middle.

At least it will get them to ponder the problem rather than just rubber stamp it. Just because you can calculate doesn't mean it actually has any value.
 

bobdoering

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#6
Re: How to calculate cpk with only a min tolerance

At its simplest, capability speaks to how well your process variation fits with the customer defined 'tolerance' or specification range. A general story used to explain Cp and Cpk is that Cp addresses whether a car will fit within a garage and Cpk addresses where in the garage the car is located.

So given that - plus the good comments Bob has made, you have a few things to consider for your situation. With a one-sided spec, you have more of a carport than a garage. :) But are being asked to use Cpk to show the fit.

Cpk by formula is = (min( USL - avg, Avg - LSL))/ 3 std dev

In your case you take the Avg - LSL to get your numerator and use 3 standard deviations for the denominator to get the ratio. So you can satisfy the expectation of producing a Cpk value.
The problem with a unilateral tolerance is that there is no roof (or walls) on the parking. All you are doing is stating how close you are parking to the side of the house - when as long as you are not parking in the house you are good. You could be parking down the street or the next town down. Cpk calculation with a unilateral tolerance shows distance from the spec in standard deviations - when it was designed to show if the mean was centered in the spec. Two different questions. In essence, all you are doing is calculating something for the sake of a rubber stamped requirement. Sure, if the data is "good", it will shut them up.

But....if it isn't....
 

kwalityguy

Involved In Discussions
#7
We calculated Cpk (actually Ppk but that's for another discussion) for one sided specifications using Statgraphics all the time. Simply leave the opposite side of the tolerance blank. In your example you would enter the lower spec of 30 inch-pound but leave the upper spec blank. Manually you would do it the same way.
 

bobdoering

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#8
We calculated Cpk (actually Ppk but that's for another discussion) for one sided specifications using Statgraphics all the time.
Yes, as I mentioned, it can be calculated. But, what it represents and the value it provides to anyone that rubber stamps the requirement to calculate it is the issue. The details above outline why, outside of sheer curiosity, it has little value. Too many people feed numbers into crunching software, get answers and have no idea what it means or if it is even correct. That makes the software a crutch, not a tool.

Don't feel bad, though. I used to do the same thing until I learned better.
 

kwalityguy

Involved In Discussions
#9
Any tool can be abused and be of little value. It's up to a professional to understand this and how to use it. We provided capability reports monthly to a customer showing each critical/significant characteristic's capability. The customer QE was responsible for dozens of suppliers with hundreds of critical/significant characteristics. The capability report would allow him to quickly identify potential problem areas. If our capability was below a given value we would get a call, maybe even a visit to find out what the problem is and what improvement actions we are implementing.

If a person who worked for me was blindly feeding numbers into software and not have a clue what the numbers mean, I'd be embarrased. We would have some special high intensity training to correct this tout de suite.
 

bobdoering

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#10
If a person who worked for me was blindly feeding numbers into software and not have a clue what the numbers mean, I'd be embarrased. We would have some special high intensity training to correct this tout de suite.
I guess the same should hold for the customers that require Cpk on characteristics that are not applicable. There is a lot of training needs to go around....
 
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