iSixSigma

6SIGMA

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  • #27709

    DAVID CHANDLER
    Participant

    WE HAVE A BIG CONTRADICTION IN OUR COMPANY WITH 6SIGMA AND STANDARD DEVIATIONS. IS IT CORRECT TO ASSUME THAT
    6SIGMA =CPK= min[(usl-u)/6*standard deviations, (lsl-u)/6*standard deviations.

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    #68168

    carper
    Member

    David:
    The correct equation for Cpk is the same as you had except that the divisor is 3 standard deviations.  Capability indices have been around longer than the “goal” of a “six sigma process”.  With the traditional calculation of Cpk, a “six sigma process” would have a Cpk score of 2.0.  This would allow for a minimum of 6 standard deviations between the mean and the nearest spec.
    Hope that helps.
    Teresa

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    #68169

    Edwards
    Participant

    Thank you very much Teresa, so at +/-3 Standard deviations i should have a 6sigma process that i will only allow me 3.4 defects.

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    #68172

    carper
    Member

    At a Cpk value of 2.0 you should only have 3.4 defects per million.  A six sigma process is still a process where you can fit 6 standard deviations between the mean and the nearest spec limit if you were to draw out a normal distribution with specs. That would give you 3.4 defects per million opportunities LONG TERM.  In six sigma language, Cp and Cpk values are based on short term estimates of standard deviation.  This means that in the long term, allowing for a shift in the mean of 1.5 standard deviations over the long term, you would only have 3.4 defects per million opportunities.  This can be a very confusing distinction without being able to draw a picture.  If you use a normal probability table and look up the probability associated with 3.4 defects per million, you will find that it equates to a Z score of 4.5.  This is because of the previously discussed 1.5 standard deviation shift in the MEAN from the short term to the long term.
    I hope that helps more than it confuses.
    Teresa
    Teresa

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