# what is the mathematical derivation for six sigma

Six Sigma – iSixSigma Forums Old Forums General what is the mathematical derivation for six sigma

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• #35498

Naga
Participant

often people say that six sigma is equal to 3,4 DPMO, and in a similar manner with all other sigmas starting from 1 to 5.
Is there any book which deals about the mathematical part of it by explaining as to how this derivatino is derived?
any help on this would be greatly appreciated.
thank you

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#100029

Bart
Participant

Hello Naga,
Sigma is a statistical concept that represents the amount of variation present in a process relative to customer requirements or specifications. When a process operates at the six sigma level, the variation is so small that the resulting products and services are 99.9997% defect free.
Best regards,Bart

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#100031

Naga
Participant

Thnx Bart!
well i do understand the basics about it, but my question is not about the end result, but about the derivation part which results to six sigma.
do u have the exact statistical steps which would bring this 99.9997% result?

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#100034

DaveG
Participant

Naga,
“Six” Sigma, in statistical terms, is the N index:  the number of standard deviations from the normal distribution mean.  In plain English, the horizontal position on the curve.  “Six” Sigma is really N = 4.5, due to the famed 1.5 sigma shift.  The area under the curve between the mean and N = 4.5 is 0.9999966 (3.4 dpm) of the total area to the right or left of the mean.

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