# Should I calculate both Cp and Cpk for a Unilateral Tolerance?

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#### Ganesh_QM

Dear Experts,

Can anyone please let me know, whether we should calculate both Cp and Cpk for unilateral tolerance ? I got this galnce when i tried to understand the difference between a target and USL for a GD & T dimension . . Can you please help me in this regard

Ganesh Moorthy

#### Kales Veggie

##### People: The Vital Few
Dear Experts,

Can anyone please let me know, whether we should calculate both Cp and Cpk for unilateral tolerance ? I got this galnce when i tried to understand the difference between a target and USL for a GD & T dimension . . Can you please help me in this regard

Ganesh Moorthy
Cp is often difficult because the distribution is not normal.

Cpk is also difficult for the same reason, especially if the process center is close to the nominal. An example would be runout or roundness.

You have to do the tests to see of CpK or Cp is valid.

#### raghu_1968

##### Involved In Discussions
For the unilateral tolerances, it is possible to calculate CpK only.

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#### Darius

whether we should calculate both Cp and Cpk for unilateral tolerance ? I got this galnce when i tried to understand the difference between a target and USL for a GD & T dimension
As it can be seen from your question, the unilateral variable has USL and you would like (or assume) that the variable must be the same value so theorically USL = Target....

Target must be the value that help us to obtain the best from out process, so if you are looking for no no-complains, it could be tricky to put it at the USL, variation must be taken in account so your would be able to spect almost no defects.

Cp, can't be calculated for one sided spec in a traditional way, Cp is how many times your process variation occupy the specs (as an area of possible values).

Cpk can be calculated for USL only = (USL-Mean)/(3Sigma), but as Kales said, many unilateral variables behave in a non-gaussian distribution, so, if that is the case, it could be better to transform the data before calculating the index or use it to compare against it self. As I remember, I have readed something like "in order to manage, one must meassure"

#### bobdoering

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Cpk should not be calculated for any true unilateral tolerance. The assumption is normal distribution and centered target value. The point of Cpk is to determine centering to the specification. The point of a unilateral tolerance is that there is no centering. Transformations or "half Cpks" (Cpu or Cpl) can be calculated, but are statistical nonsense to the point of calculating Cpk, so should not be reported.

If a customer expects this data on a unilateral tolerance, you can rest assured they are using the Cpk "rubber stamp", and have no statistically supported rational for the request.

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#### Ganesh_QM

Thank you for your response . So can i proceed with Cpu for position tolerance ??? If that make sense then i would take it forward to our customer !!

#### bobdoering

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Thank you for your response . So can i proceed with Cpu for position tolerance ??? If that make sense then i would take it forward to our customer !!
If your goal is to satisfy a statistically illiterate customer, then you can give them that data. Again, it is fundamentally nonsense.

If they are automotive, and subscribe to TS16949, I would tell them to read closely PPAP 4th edition 2.2.11.5.

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#### Darius

The point of Cpk is to determine centering to the specification. The point of a unilateral tolerance is that there is no centering.
:truce:I am agree, Cpk is a statistical nonsence but not only for unilateral, if people try to correlate it to ppm or ppb, look at the calculation, the minimum of (USL-Mean, Mean-LSL)/(3Sigma).
What give it to us?,
Minimun(USL-Mean, Mean-LSL) give us the minimum distance of our process centering to the spec
and
3Sigma is the distance from the process centering to the control limit (or as Wheeler may say "natural limits").
so Cpk is how many distances from the Center of the process is the Spec limit, is a measure, just that, Wheeler said in "Advanced topics on SPC", the best is forget about indicators, if you try to determine defective, calcule them directly.

As I say before, "to manage, one must measure", agree that is a faulty indicator, but is there another option?, a better aproach could be to chart box-charts across the time, but how to measure improvement?, no measure is better that a faulty?, not sure.

note: I use something like that when I try to determine if a value is "strange" , but the value insteed of the process mean, and work as a charm.

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#### bobdoering

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:truce:I am agree, Cpk is a statistical nonsense but not only for unilateral, if people try to correlate it to ppm or ppb, look at the calculation, the minimum of (USL-Mean, Mean-LSL)/(3Sigma).
What give it to us?,
Minimum(USL-Mean, Mean-LSL) give us the minimum distance of our process centering to the spec
and
3Sigma is the distance from the process centering to the control limit (or as Wheeler may say "natural limits").
so Cpk is how many distances from the Center of the process is the Spec limit, is a measure, just that, Wheeler said in "Advanced topics on SPC", the best is forget about indicators, if you try to determine defective, calculate them directly.
Cpk, as determined by largest of Cpu, Cpu adds the clue as to how centered the distribution mean is to the specification that Cp does not (assuming "centered" is truly valuable). To only calculate one or the other for a unilateral specification does, as you say, solely provides a distance from the mean (no longer the center) to the spec. Distance versus degree of being centered...two unrelated questions, only one of which Cpk is not designed to answer. So, it can be calculated, but answers the wrong question.

For one number to describe the process variation over time of any process is so much of a stretch, I have no idea how it EVER got any traction in quality. Fold into that the data was likely taken incorrectly (such as one diametric measurement for a circular feature) that it slips further into the realm of fiction.

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