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PPM defects for 1.1 Cpk

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  • #52011

    Herb
    Participant

    Two processes have identical Cpk, which produce 966 ppm defects.  One process is perfectly centered, while the other is halfway between the center of the tolerance and the LSL.  Would both processes still produce the same number of defects?  The off center process would seem to only produce defects on the lower tail side versus the perfectly centered process producing defects on both tails.  Help!

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    #182253

    Mikel
    Member

    Correct

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    #182254

    Herb
    Participant

    What is correct, they produce the same number of defects or the off center process would produce less?  Please explain a bit more for the theory side.  Are you considering just this point in time, any 1.5 sigma shift over time, etc.?

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    #182255

    MrMHead
    Participant

    No No NO!  Don’t Mention S**FT  It’s a 4 letter word in this forum!  ;-)
    As for the More or Less defects between centered and non-centered:
    It Depends!  If the non-centered process has a smaller StdDev (spread), then it could very well have fewer defects than a centered process with a larger StdDev.
    I ran into a process where we initially thought it was a Spread (variation) problem, but the center was actually above the USL. So fixing spread in that instance would have made things worse. – and it wasn’t just in class.

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    #182256

    Herb
    Participant

    If both processes had the same tolerance, then the shifted process would have to have a smaller std dev in order to achieve the same Cpk.  Forgot any mention of the previous “5 letter word”.  Statistically, the defects may be smaller for the shifted process, but practically speaking, is the difference even worth the mention?

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    #182257

    MrMHead
    Participant

    If you are just reporting/ comparing Cpk, the center and spread are not seen by the customer.
    If you are looking to improve Cpk, then you would further examine center and spread.  Is the “centered” process truely a “Normal” curve?  Or is it skewed or long-tailed on one side . . etc
    What would be the effective impact if you improved Center on the non-centered process?  Is it more feasable (cost effective) to improve Spread for a better Cpk?
    Can you move your process to a geographic location with a smaller shift according to hbgb’s (?) taxonomy of continental shift values  ;-)

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    #182259

    Herb
    Participant

    If my process were not normal, then the Cpk would have little,  if any validity at all.  After reviewing the calculations for Cpk, I would predict the PPM out of spec would be the same for either process.  The improvement method would be much easier for the shifted process, as long as the adjustment to center was simple.  Reducing the spread of the “centered” process would probably take a little more work.  Thanks for all the input.

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    #182263

    MBBinWI
    Participant

    My esteemed colleagues:  I believe that you missed the question.  It was, for two processes with identical Cpk, one perfectly centered, the other 1/2 way to the spec limit, which is producing more defects.  The answer is easy (assuming a normally distributed process), since Cpk is only calculated based on the closest spec limit, the centered process is producing twice the number of defects as the non-centered process.  This can be observed by simply drawing the distributions.  For the off-center process you will see that the width of the distribution is considerably narrower than the perfectly centered distribution.  You will also observe that the other side of the off-center distribution has gone so close to zero as to be considered zero.  For the centered process, the defects for Cpk are only counted on one side, but exactly the same number will exist on the other side!  So, in reality, the effective Cpk is much lower.  Although not the question, as others have indicated, the off-center process is also likely to be much easier to improve, as it is usually an easier task to adjust settings to affect the mean than to reduce the variation.

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