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Z term VS Sigma

Six Sigma – iSixSigma Forums Old Forums General Z term VS Sigma

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  • #36319

    newb
    Participant

    can anybody please explain the difference between sigma and Zst/lt.  I mean i know sigma is the deviation and my understanding is Z is a measure of predictability.  Why would some people only measue sigma and others only use Z?
    thanks
     
     

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    #104607

    newb
    Participant

    so yeah this is a shameless bump to the top.  this is like one of the least complex questions i’ve seen on this board and everybody ignored it!  Everybody too good to answer newbie questions?  :)
    Thanks for your help
     

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    #104614

    Marz
    Participant
    #104617

    Nick Ruhman
    Participant

    Z term is simply the result of taking the distance from the mean to a point of interest (most cases the spec limit) and dividing it by the standard deviation.  This is done so that we can use the probabilitys from the standard normal distribution and it’s Z values for an apples to apples comparison. 
    Simply put, all normal distributions have the same area’s under their curves to the left and right for a certain Z score, no matter what the mean and standard deviation.  So we need the Z score to calculate expected PPM’s.  Cpk’s are simply the Z score divided by 3. (How many 3 SD’s fit between the mean and closest spec limit)
    Nick

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    #105609

    Schuette
    Participant

    The Z transform is (mean-x)/SD which results in a N(0,1) distribution.  I first incountered the Z transform in the education field.  When two classes are graded on different scales, there is not an easy way to compare or combine the resulting grades.  If you transformed both classes grades with the Z transform, then both classes are on equal footing.  That is a N(0,1).

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    #109634

    Glenn
    Participant

    Nick,
    I’m alittle confused with your response. Are you saying that the sigma level and the Zst are different? The Zst is based on the spec limit and the sigma level is some other criteria? I was taught that the sigma level and the Zst were the same. Will you explain?

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    #109944

    Nick Ruhmann
    Participant

    Yes and No. Technically, you can caluclate the sigma level for ANY POINT OF INTEREST. It just so happens that most of the time that point of interest is a specification limit. But it doesn’t mean that I can’t calculate a sigma level for any value I so choose, as long as I specify that.
    Assuming your point of interest is the specification limit, then yes they are the same. Some 6 sigma training may teach the formula for Sigma level using the specification limit specifically, I just know that the training I received had the term “point of interest” in the formula. We played with many points before then applying it to the specification limit. If someone says the sigma level of a process is 3 sigma, ie 1 Cpk, it would be assumed that they are referring to the closest specification limit.Sorry if the terms I used were confusing.
    Nick

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