


15th July 2003, 09:50 AM


Calculating Cpk on a single sided (unilateral) tolerance
Calculating Cpk on a single sided tolerance
Okay I have a diameter that is .250” +0.010” (note there is no minus), how do I calculate Cpk? And is it possible to calculate Cp as I think it is not based on the Cp equation (USL – LSL / 6 standard deviations). In this instance there is only size – plus, and not size plus and minus.
Also, is there an excel formula for the Cpk calculation (if poss)
Best Regards
Lee01
Last edited by lee01; 15th July 2003 at 09:53 AM.

15th July 2003, 10:39 AM


The issue of Cp and Cpk has been debated a great deal recently. Do a search for more info.
If the spec.is .250"  .260", consider the possibility of using a spec. of .255' +/ .005" for your spec. in calculating Cpk.

15th July 2003, 10:42 AM


Lee,
In case you have a one sided tolerance (let's say upper tolerance only), the Cpk is evaluated as Cpk upper. Cp is not defined in such cases.
However from what you have written, it does look as though you really have a two sided tolerance. The tolerance is expressed on the plus side only as a convention (like in a hole basic system). Would it be acceptable for instance, if your diameter went below 0.250" ? It could even go to zero if you don't really specify a lower tolerance and the hole or the shaft under consideration would completely vanish.
A two sided Cp/Cpk formula would apply here.
One sided tolerances are typically found in parameters like surface roughness, breaking strength, and form tolerances like straightness, flatness, roundness and cylindricity.
Hope this helps.
Ravi

15th July 2003, 10:54 AM


As Mike said "The issue of Cp and Cpk has been debated a great deal recently. Do a search for more info."
In
http://Elsmar.com/Forums/showthread.php?t=6410
I posted, that Cpm, or Cpmk are in my opinion better capability index than Cp, Cpk for one sided spec.
The problem that I saw in Cpkl or Cpku for one sided spec is that they don't take the target in account, and "Quality is to the target with the minimum variation".

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


16th July 2003, 07:32 AM


Ravi,
This is a single sided tolerance as the size described is 0.250 + 0.010. This means that obviously it cannot be below the .250 size.
I have been told that there is an equation that takes into consideration the Skewness and Kurtosis to give a value, this value is then used to calculate Cpk.
Help please
Lee01

16th July 2003, 07:55 AM


Lee,
1. If the size cannot go above 0.260 (0.250 + 0.010), the Upper Spec Limit = 0.260
2. If the size cannot go below 0.250 (as referred by you above), the Lower Spec Limit = 0.250
Any parameter that has both, USL & LSL is to be treated as a two sided tolerance.
To determine Kurtosis and skewness, you will have to look at the histogram. Kurtosis describes the peakedness of the distribution. Skewness describes whether the distribution is lopsided.
If you have to determine the process capability using a Non Normal distribution there are methods to transform the data. You could look up Pearson and Johnson families of distributions for this.
Ravi

Thanks to Ravi Khare for your informative Post and/or Attachment!


12th August 2003, 05:36 PM


Lee, I think the confusion you're running into is between a singlesided tolerance which has only one direction that it can go, such as speed (i.e. you can never go slower than 0), and a unilateral tolerance, or unevenly distributed tolerance in which you may want the result to be closer to one end than the other, but is still possible to go out of spec on both ends.
To say that the hole size cannot go below .250 is more of a technicality. It can go below .250, but it should not due to design requirements, thus it is a twosided tolerance with uneven distribution of the tolerance limits.
Quote:
In Reply to Parent Post by lee01
Ravi,
This is a single sided tolerance as the size described is 0.250 + 0.010. This means that obviously it cannot be below the .250 size.
I have been told that there is an equation that takes into consideration the Skewness and Kurtosis to give a value, this value is then used to calculate Cpk.
Help please
Lee01


12th August 2003, 11:36 PM



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