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Where does 3.4 parts per million come from?

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  • #30700

    boettler
    Member

    How is this number derived?
     

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    #80345

    Cravens
    Participant
    #80347

    Jamie
    Participant

    Convert 3.4 DPMO to percent (i.e. 3.4/1,000,000) and look up the right tail area in a Standard Normal Table (most tables don’t go this far, so you will probably need one asscociated with Six Sigma). You will get 4.5 standard deviations.
    Now add 1.5 to this and you get 6 Sigma. We add 1.5 because the general assumption for calculating sigma level is that you have long term data (it represents most of the systems variation) but want to estimate short term Sigma (i.e. what the customer is likely to see at any given time… from a batch or run or order). Past studies have shown that short term sigma level is general 1.5 Sigma better then long term.
    This is how 3.4 DPMO equates to Six Sigma.
    Jamie
     

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    #80349

    John Twist
    Participant

    Taken from: http://www.lmu.ac.uk/lis/imgtserv/tools/sixsigma.htm
    A Six Sigma quality level is said to equate to 3.4 defects per million opportunities. This is actually a little strange since if a normal distribution table is consulted (very few go out to six sigma), one finds that expected nonconformances are 0.002 parts per million (two parts per billion). The difference between this figure and the ‘official’ six sigma figure of 3.4 defects per million parts is because, when the concept was established, it was assumed that a typical process mean could drift 1.5 sigma in either direction. The area of a normal distribution beyond 4.5 sigma from the mean is indeed 3.4 parts per million. Because control charts will easily detect any process shift of this magnitude in a single sample, the 3.4 parts per million represents a very conservative upper bound on the nonconformance rate.

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