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Capability Calculations for Unilateral Specifications

Discussion in 'Capability - Process, Machine, Gage …' started by Bob Doering, Apr 18, 2016.

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Did you know that Cpk is not a correct capability index for a unilateral specification?

Poll closed Jul 18, 2016.
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  1. Bob Doering

    Bob Doering Member

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    Some people like to default to the "half Cpk" approach (report Cpu or Cpl) when forced to calculate capability for a unilateral specification. The problem is, it really does not make any sense. The difference between Cp and Cpk is that Cpk answers the question "is the distribution mean centered?" For a unilateral specification, that is a nonsensical question. The target is usually 0, not the center of the specification tolerance. What a "half Cpk" represents is the distance of the mean from the specification. The problem is, nobody is asking that question...they are asking if it is centered. For those in automotive, refer to PPAP 4th edition section 2.2.11.5 Note that tells you Cpk does not apply to unilateral specifications! See the attachment for further discussion.
     

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  2. Chris Glover

    Chris Glover Active Member

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    I have been fighting this battle for years!
     
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  3. ncwalker

    ncwalker Well-Known Member

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    To make matters worse, these unilaterals are typically geometric tolerances - form data. That's typically a Weibull distribution. So ... right there you don't have your normality requirement.

    And even worst than that, they want it on true position data, which is totally ridiculous to just calculate even CpU on a bunch of position results.

    But, sometimes my customer demands (and pays for) stupid data. And we supply it. (And die a little on the inside every time ...) The strangest part? When we get into one of these battles where we will never get some weird result in some arbitrary limits because the math doesn't describe the world, it never gets resolved. It usually just lingers as an open issue until everyone is tired of it and we silently agree to let it fade away ....
     
  4. Bob Doering

    Bob Doering Member

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    Yes, I usually get a Weibull or beta distribution with form data. You CAN get a normal distribution if your data is so far away from the physical limit that it has no effect on it! So, the more normal your data is, the worse the condition is! Sometimes I like to train my customers, but there are some hopeless ones out there with the big statistics rubber stamp.
     

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