In teaching Six Sigma workshops at Dartmouth, we assure that everyone understands that "Six Sigma" as it is presented in the industry, is in fact mathematically 4.5 sigma. So when folks say "Six Sigma" is 3.4 defects per million (dpm), they are not really referring to plus and minus 6 standard deviations from the mean (even though they may not know it), as 3.4 dpm is only 4.5 sigma. The true 6 sigma defect rate is 2 defects per billion. The figure above shows this error.
Where did this confusion come from? When "Six Sigma" was first developed, it was defined as a Cp of 2 and a Cpk of 1.5. These process capability indices are were the confusion lies. A Cpk of 1.5 allows for a shifting of the process mean of 1.5 sigma, hence the true statistical measure of Cpk = 1.5 is 4.5 sigma or 3.4 ppm. True statistical six sigma (Cpk = 2) is elusive indeed at 2 dpb!