

27th April 2013, 03:06 AM


One Sided Tolerance Distribution(s)
Hello everyone,
First many thanks for the incredible job done here. This is my first post, but this forum already helped many times before today...
I know the question of process capability for one sided tolerance characteristics was discussed before (maybe more than once). However, there is still something bothering me that I can't figure out. It's not only about how to calculate the capability though...
The following are my personal conclusions, so please correct me if I am wrong:
There are two types of characteristics with one sided tolerance:
1 With natural "limit": for example perpendicularity or flatness. These cannot have a value less than 0 and therefore have only the upper tolerance. These characteristics should follow a folded normal distribution. Right?
2 Without natural "limit", but rather with only one actual specification: for example tensile strength which should not be less than X MPa (lower tolerance), but that can go up to whatever value possible. These characteristics should follow a normal distribution, right? Or is there any other specific distribution for these cases (one sided normal distribution for example)?
Is the Cpk calculated the same way in both cases anyway? And is the calculation based on the same dispersion used for normal distribution (3*sigma)?
Once again, thanks for the great job.
Uchiha

29th April 2013, 05:01 AM


Re: One Sided Tolerance Distribution(s)
A Quick Bump!
Can someone help?
Thank you very much!

29th April 2013, 07:54 AM


Re: One Sided Tolerance Distribution(s)
Quote:
In Reply to Parent Post by Uchiha
There are two types of characteristics with one sided tolerance:
1 With natural "limit": for example perpendicularity or flatness. These cannot have a value less than 0 and therefore have only the upper tolerance. These characteristics should follow a folded normal distribution. Right?

Not necessarily. If the "natural limit" is artificial, such as Position where you are using the (polar) absolute value of the x/y coordinates that may actually be negative, or flatness that does not distinguish between concave/convex then you will likely have a folded distribution. However, if the natural limit is real as you would get by machining to a hard stop, you would be more likely to get a lognormal or similar distribution.
Quote:
In Reply to Parent Post by Uchiha
2 Without natural "limit", but rather with only one actual specification: for example tensile strength which should not be less than X MPa (lower tolerance), but that can go up to whatever value possible. These characteristics should follow a normal distribution, right? Or is there any other specific distribution for these cases (one sided normal distribution for example)?

The tensile strength distributions that I have worked with have all tended to be skewed. By theory, they should follow a smallest extreme value (i.e., weakest link) distribution.
Quote:
In Reply to Parent Post by Uchiha
Is the Cpk calculated the same way in both cases anyway? And is the calculation based on the same dispersion used for normal distribution (3*sigma)?

No. You should perform a nonnormal capability study.
Some would advise that you transform your data using a BoxCox transform, but I do not recommend this. I work with the native distribution.

Thanks to Miner for your informative Post and/or Attachment!


29th April 2013, 09:21 AM


Re: One Sided Tolerance Distribution(s)
Quote:
In Reply to Parent Post by Uchiha
1 With natural "limit": for example perpendicularity or flatness. These cannot have a value less than 0 and therefore have only the upper tolerance. These characteristics should follow a folded normal distribution. Right?

Typically, through distribution fitting, I find the most typical disttributions for onesided physical limit tolerances to be beta or Weibull distributions.
Quote:
In Reply to Parent Post by Uchiha
2 Without natural "limit", but rather with only one actual specification: for example tensile strength which should not be less than X MPa (lower tolerance), but that can go up to whatever value possible. These characteristics should follow a normal distribution, right? Or is there any other specific distribution for these cases (one sided normal distribution for example)?

There really is no locationspecific capability (as in Cpk or Ppk) for onesided distribution, as the whole point of their existence is to determine if the mean of the distribution is near the center of the tolerance. However, the center is not the goal of a onesided tolerance, so the point is moot and nonsensical. You can use Cp or Pp.
Quote:
In Reply to Parent Post by Uchihi
Is the Cpk calculated the same way in both cases anyway? And is the calculation based on the same dispersion used for normal distribution (3*sigma)?

No, Cpk is not applicable to either. Cp or Pp can be calculated via transformation.

29th April 2013, 01:14 PM


Re: One Sided Tolerance Distribution(s)
Why even do distribution based Cp/Pp/Cpk/Ppk? why not just plot your data in time sequence against the specificaiton limits? this will tell you how 'capable' you are. If you are producing defects, a simpel defect rate calculation should be sufficient to quantify the 'incapability'. What infromation will you derive from a "CPpk" calculation? what actions will it drive? Is it really worth all of the time spent figuring out how to calculate it? isn't it better to spend your time in actually improving the capabilty? just a thought...

Thank You to Bev D for your informative Post and/or Attachment!


29th April 2013, 01:38 PM


Re: One Sided Tolerance Distribution(s)
Quote:
In Reply to Parent Post by Bev D
Why even do distribution based Cp/Pp/Cpk/Ppk? Why not just plot your data in time sequence against the specification limits? This will tell you how 'capable' you are.

I agree. Once the process is in place, it is more about what happens over time. In fact, a correctly implemented SPC charting method would be even better, if applicable.
Quote:
In Reply to Parent Post by Bev D
What information will you derive from a "Cpk" calculation? What actions will it drive? Is it really worth all of the time spent figuring out how to calculate it? Isn?t it better to spend your time in actually improving the capability? just a thought...

That's correct. In fact, in precision machining capability is a constant...no need to continue to calculate.
If the supplier is not sophisticated or lacks resources for data tracking, there is one easy way around the issue. Cut back the spec to 75% of the original spec. Perform you incoming verification to the full spec, and a lot of problems should disappear. There is a statistical justification for this based on the total variance equation, but without going into all of that, it should improve your issues.

Thanks to bobdoering for your informative Post and/or Attachment!


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