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How is DPMO converted to Sigma

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  • #28213

    hoon
    Participant

    There is a six sigma conversion table in the book of “The Six Sigma Way : How GE, Motorola, and Other Top Companies Are Honig Their Performance by Peter S. Pande, Robert P. Neuman, Roland R. Cavanagh.
    Β I wonder how DPMO is converted to sigma.Β  Anyone can help me?
    Thank you.

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    #69932

    Jaran S.
    Participant

    1. Calculate DPMO for each sigma level, using 1.5 sigma shift
    Β Β Β  assumption. It is based on normal distribution assumption also.
    2. You can get the relation betweenΒ sigma level and DPMO.
    3. When you get any DPMO, then I estimate sigma level by using the
    Β Β Β Β relation you get.
    4. This may not be valid but it is the way to express process capability
    Β Β Β  withΒ attribute data into same process capability unit,Β sigma level.
    Jaran S.

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    #69934

    Bonnie Paris
    Participant

    I recommend that you check out the

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    #70002

    hoon
    Participant

    Thank you Jaran S. and Bonnie Paris.
    Β 

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    #70028

    EMiller
    Participant

    Hoon –
    My company produces software for just this purpose.Β  Please browse to http://www.hertzler.com/html/prod_dms.aspΒ for information, or send me an email at [email protected].Β  You might also find this page useful: http://www.hertzler.com/html/prod_6sigma.asp.
    Regards,
    Evan

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    #70042

    schaeffers
    Member

    Dear Mr Hoon,
    The sigma is calculated by transforming the defects to a normal distribution. There is a formula to do it. However you can just use the sigma calculator. This is freeware software which converts defects, subgroupsizes and opportunities to a sigma number. In the help screen you can also find the sigma conversion table. You can just download this freeware from http://www.spcwizard.com look for the 6 sigma page.
    Β 
    Β 

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    #70053

    SixSigmaGuy
    Participant

    I wanted to add to the other replies that you don’t always want to include the 1.5 sigma shift. It depends on the process you are working with. For example, with Transactional processes you don’t want to do the shift.

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    #70075

    Ken K.
    Participant

    Using:
    SigmaΒ =NORMINV(1-DPMO/1000000,1.5,1)
    The Excel NORMINV function’s estimate of Sigma is accurate to two decimal places between 1.4 and 5.7 Sigma. It is accurate to one decimal place between 5.7 and 6.1 Sigma.
    Using a much longer formula:
    Sigma =SQRT(LN(1/(1-EXP(-DPMO/1000000))^2))-(2.55155+0.802853*SQRT(LN(1/(1-EXP(-DPMO/1000000))^2))+0.010328*SQRT(LN(1/(1-EXP(-DPMO/1000000))^2))^2)/(1+1.432788*SQRT(LN(1/(1-EXP(-DPMO/1000000))^2))+0.189269*SQRT(LN(1/(1-EXP(-DPMO/1000000))^2))^2+0.001308*SQRT(LN(1/(1-EXP(-DPMO/1000000))^2))^3)+1.5
    This “long” formula is accurate to two decimal places between 3.2 and 9 Sigma. It is accurate to one decimal place between 2.5 and 3.2 Sigma. It should not be used below 2.5 Sigma or above 9 Sigma.

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    #70121

    Ricardo Moura
    Member

    Hi,if you have the DPM or DPMO, you can obtain the sigma level without any specification limits, using the following equation:sigma level = 0.8406 + sqrt[29.37-2.221*ln(DPM or DPMO)](sqrt=square root and ln=natural logarithm)this equation returns the sigma level + 1.5 sigma shift, and we can assign then to the “sigma capability”. If you don’t want the sigma shift, you can subtract 1.5Bye,Ricardo.

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    #70129

    SixSigmaGuy
    Participant

    This is great. Does it mean I can throw away my tables? :-)

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