When learning about Six Sigma, it may help to consider these charts, which detail how sigma level relates to defects per million opportunities (DPMO), and some realworld examples.
Sigma Performance Levels – One to Six Sigma  

Sigma Level  Defects Per Million Opportunities (DPMO) 
1  690,000 
2  308,537 
3  66,807 
4  6,210 
5  233 
6  3.4 
It’s one thing to see the numbers and it’s a whole other thing to see how it would apply to your daily life.
Realworld Performance Levels  

Situation/Example  In 1 Sigma World  In 3 Sigma World  In 6 Sigma World 
Pieces of your mail lost per year [1,600 opportunities per year]  1,106  107  Less than 1 
Number of empty coffee pots at work (who didn’t fill the coffee pot again?) [680 opportunities per year]  470  45  Less than 1 
Number of telephone disconnections [7,000 talk minutes]  4,839  467  0.02 
Erroneous business orders [250,000 opportunities per year]  172,924  16,694  0.9 


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Comments
why do you mean 3.4 ppm as six Sigma
3.4 ppm means that the opportunities or likelihood that the product/process will fail is 3.4 in a million. like for an instance when you bought a single lottery ticket. the chances of winning is only 3.4 out in a million or 0.00034%. in terms of defects the chances that the single product/process fails is only 3.4 out in a million. it is totally different of saying that producing one million parts you are expecting 3.4 defects which a lot of people misinterpret.
why can,t we say that seven sigma or eight sigma instead of six sigma? or explanation of Six?
Six sigma 3.4 ppm mean 3.4 defect per million opportunity.
It means 99.99966 % data falls withing specification. so that 10099.99966=0.00034% = 3.4 ppm
no wrong !, 3.4 doesn’t mean 0.00034% defects or 99.99966% good
6 means 99.9997 % good
and there are six [6] sigma levels not 3.
calculated as
[ defect units / (no. of oppertunities * no. of units) ] * 1,000,000
But U know that in calculating of actual capability metrics the normal distribution is from 3s to +3s (centered process). In there are about 99,….% probability of execute products is six sigma level quality. So, from 3s to +3s there is 6 sigma. I must say that in banking exist 7 sigma level.
Thank you for your comments. I see that Six Sigma represents a measurement for the number of defects in a near perfect level of performance in anything we can do.
Defect counts are like random variables representing deviation from mean. They follow bell curve (normal distribution) and have a mean (mu) and a standard deviation (sigma) like any other random distribution.
By counting defects per million you can judge the quality maturity of your process in units of one two three or six times the standard deviation (sigma).
1 2 3 6 sigma = 68% 95% 99.7% and 99.9999998% (percentage of total area under normal bell curve)
http://en.wikipedia.org/wiki/Normal_distribution