# 6 Sigma = 3.4 Defects Per Million?

Six Sigma – iSixSigma Forums Old Forums General 6 Sigma = 3.4 Defects Per Million?

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• #30504

chencan
Participant

All documents related Six Sigma claims that Six Sigma means 3.4 defects per million.  However, if we use MS Excel to run a simple function named NORMSINV (0.9999983) which means the a/m 3.4 PPM, the result is 4.619.  That is to say, with + 4.619 sigma between the mean, we can already achieve 3.4 PPM, rather than widely known 6 sigma.
Moreover, if we use + 6 sigma to do the reversed function NORMSDIST (6), the result is 0.999999999.  That means only  1 defect out of 1 billion rather than 3.4 out of 1 million.
In view of the a/m simple calculation, I got quite confused that 6 sigma equals to 3.4 PPM?  Any expert can help me out of this confusion?
Thanks and Best Regards,
Chen Can

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#79505

Robert Butler
Participant

You are correct with respect to your computations.  A Z score of 4.5, as you noted, does correspond to 3.4ppm.  The Six Sigma claim of 3.4ppm at a Z score of 6 is due to the simple fact of adding 1.5 to the Z score that you would get from a cumulative normal table.
The justification for the addition of this 1.5 factor rests on three studies that were done 25 and 50 years ago.  Probably the best (and most recent) discussion of the reasons for this addition can be found in Quality Engineering 14(3) pp.479-487 in an article by Davis Bothe-Statistical Reason for the 1.5 sigma Shift It is an excellent and very readable article. It is the sort of paper that should be committed to memory by anyone claiming any expertise in the world of SixSigma quality

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#79506

S Vijayaraghavan
Member

Hi Chen,
It is Correct that 4.5 sigma level of “Process Capability ” itself  is sufficient to  achieve 3.4 defectd per Million opportuniiies. However every process has a long term drift and conventionally the drift (To cater for long term variations) is stated to be +/- 1.5 Sigma. Hence a process capability of 6 Sigma (4.5 +1.5 for drift) is necessary to achieve a sustained performance of  3.4 defects per million opprtunities.
Rags
(S Vijayaraghavan),
Green Belt, BB Candidate
Software Solution Lab, Bangalore
Honeywell

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#79547

chencan
Participant

Hi, Mr. Robert,