# Calculating Cpk on a single sided (unilateral) tolerance

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#### lee01

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

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#### Mike S.

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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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#### Ravi Khare

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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#### Darius

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".

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#### 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.

Lee01

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#### Ravi Khare

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

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#### Dave Dunn

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.

lee01 said:
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

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#### Thomas_Crown

Single sided gauges,

We have had these in the form of hole position using GD&T (a diametric gauge) Where it can deviate from its nominal in any 360 degree direction.

In a similar manner that perhaps a call centre will respond to a qaury, it can only answer it in from the time it gets the call, not before.

We use the Cp to monitor the process, and Cpu (Cp upper) for the process in relation to the desired tolerances

Thomas

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#### santhosh_mech

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

Its very simple, conver the .250 diameter to 0.255" ± 0.005" and take SPC for that parameter, U can get the Cp and Cpk