The normal probability distribution predicts a 0.00034 percent defect rate when the nearest specification limit is 4.5 standard deviations away from the process average. That’s 3.4 parts-per-million (PPM).
So why does Six Sigma require six standard deviations between the mean and the nearest specification limit? The reason is that the process average is likely to shift over the long run. Six Sigma accounts for this mean-shift up-front, by assuming a maximum mean-shift of 1.5 standard deviations (sigmas) over the long run.
While the validity of the 1.5 sigma mean-shift value can be debated for any given process, it is accepted as a sound, conservative approach for assuring a defect-free (theoretically 3.4 PPM) process over the long run. It’s easy to get wrapped up in the statistics behind the Six Sigma philosphy, but lasting results depend mostly on sound execution of the DMAIC methodology. If the underlying causes of variation are understood and controlled, we have a good shot at a long term, defect-free process.