The Elsmar Cove Business Systems and Standards Discussion Forums Calculating Cpk on a single sided (unilateral) tolerance
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# Calculating Cpk on a single sided (unilateral) tolerance

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Post Number #1
15th July 2003, 08:50 AM
 lee01 Total Posts: 89
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 08:53 AM.

Post Number #2
15th July 2003, 09:39 AM
 Mike S. Total Posts: 2,023
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.
Post Number #3
15th July 2003, 09:42 AM
 Ravi Khare Total Posts: 70
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
Post Number #4
15th July 2003, 09:54 AM
 Darius Total Posts: 551
As Mike said "The issue of Cp and Cpk has been debated a great deal recently. Do a search for more info."

In

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!
Post Number #5
16th July 2003, 06:32 AM
 lee01 Total Posts: 89
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.

Lee01
Post Number #6
16th July 2003, 06:55 AM
 Ravi Khare Total Posts: 70
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!
Post Number #7
12th August 2003, 04:36 PM
 Dave Dunn Total Posts: 131
Lee, I think the confusion you're running into is between a single-sided 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 two-sided 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
Post Number #8
12th August 2003, 10:36 PM
 Marc Total Posts: 25,191

 The Elsmar Cove Business Systems and Standards Discussion Forums Calculating Cpk on a single sided (unilateral) tolerance

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