Alin, I think there is interesting informations in your link, I will read.

Sixsigmais: Thanks for the formulas. I have also modified the shifted fbut I make the error to multiply the result by 2, which makes me confused.

The unshifted formula gives exactly the same results provided by a statistical software.

But still confused why the ppm level is doubled (excep at 4.5 sigma) in the previous unshifted tables....thing that I'm unable to simulate with a statistical software even with a centered double sided distribution...

The tables seem to be full of mistakes, so don't worry too much about them.

Products can be above spec of below spec. In principle you should calculate the upper and lower tail for every case. However, when one tail is farther from the center than the other, then the far tail can typically be ignored.

Attached is a simple spreadsheet with sigma levels, defects in the close tail, the far tail, and total defects. You can set the shift to see how many defects are in each tail. For SHIFT = 0 you get the traditional values. For SHIFT = 1.5 you get the "Six Sigma" values. Even SHIFT = 0.1 will make the close tail considerably bigger than the far tail.

I'm thoroughly impressed. I've looked for this conversion on and off over the years. I even asked a professor from a college in Dayton and he could only quote the emperical rule. Thank you for your help. I only hope that I can help someone else someday.