The Elsmar Cove Forum Calculating Cpk on a single sided (unilateral) tolerance
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#1
15th July 2003, 08:50 AM
 lee01 Courtesy Access   Registration Date: May 2001 Location: Europe and beyond (aka a nomad!) Age: 37 Posts: 89 Thanks Given to Others: 2 Thanked 3 Times in 3 Posts Karma Power: 62 Karma: 40
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.

#2
15th July 2003, 09:39 AM
 Mike S. An Early 'Cover'   Registration Date: Mar 2002 Location: East Coast US Posts: 1,858 Thanks Given to Others: 42 Thanked 118 Times in 81 Posts Karma Power: 240 Karma: 2194
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.

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#3
15th July 2003, 09:42 AM
 Ravi Khare Involved - Posts   Registration Date: Dec 2001 Location: Pune, India Age: 53 Posts: 70 Thanks Given to Others: 0 Thanked 3 Times in 3 Posts Karma Power: 59 Karma: 58
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

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#4
15th July 2003, 09:54 AM
 Darius Appreciated Information Resource   Registration Date: Mar 2002 Location: Monterrey Mexico Age: 52 Posts: 530 Thanks Given to Others: 69 Thanked 224 Times in 148 Posts Karma Power: 111 Karma: 3551
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!
#5
16th July 2003, 06:32 AM
 lee01 Courtesy Access   Registration Date: May 2001 Location: Europe and beyond (aka a nomad!) Age: 37 Posts: 89 Thanks Given to Others: 2 Thanked 3 Times in 3 Posts Karma Power: 62 Karma: 40
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
#6
16th July 2003, 06:55 AM
 Ravi Khare Involved - Posts   Registration Date: Dec 2001 Location: Pune, India Age: 53 Posts: 70 Thanks Given to Others: 0 Thanked 3 Times in 3 Posts Karma Power: 59 Karma: 58
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

__________________

If you cannot measure it, you cannot improve it.
 Thanks to Ravi Khare for your informative Post and/or Attachment!
#7
12th August 2003, 04:36 PM
 Dave Dunn Involved - Posts   Registration Date: Jul 2003 Location: River Falls, Wisconsin Age: 45 Posts: 131 Thanks Given to Others: 1 Thanked 31 Times in 24 Posts Karma Power: 60 Karma: 757
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
#8
12th August 2003, 10:36 PM
 Marc Your Elsmar Cove Host   Registration Date: Jan 1996 Location: West Chester - Southern Ohio - USA Age: 64 Posts: 24,144 Thanks Given to Others: 9,583 Thanked 5,245 Times in 3,315 Posts Blog Entries: 4 Karma Power: 400 Karma: 32367

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 The Elsmar Cove Forum Calculating Cpk on a single sided (unilateral) tolerance

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