why 3.4 parts per million ?

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January 27, 2002 at 6:57 am #28631

Murray
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One of my puzzling aspect of the “official” Six Sigma literature is that, a process of operating at Six Sigma levels will produce 3.4 parts-per-million nonconformance. I was wondering, how actually did they arrive at that figure ‘3.4’?

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January 27, 2002 at 7:17 am #71584

Sridhar
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Hi,
This 3.4 comes from the normal distribution curve. You check a stad normal distribution curve at 4.5 sigma value. Multiply the area outside this curve by one million you get 3.4. You may ask why we take 4.5 instead sigma.
Then 1.5 sigma assumed as long term shift. That is the process may shift 1.5 std deviations in the long term. That is why we have considered 4.5 sigma giving 1.5 shift. If you consider actual 6 you get 2 parts per billion instead 3.4 parts per milllion.
hope this helps you
regards
A.Sridhar

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