Quote from my classmate Gary’s post

“Well, this magic number came from the assumption of normal distibution, that most occurances will be in the middle of the range and then spreads off in a bell-shape on the chart, and Sigma is the SD of such.

So by definition 99.99999980268% of total value would lie within Mean +/- 6 x Sigma. Then, one obvious follow-up question would be why 3.4 instead of 0.002, following that logic. For this, let me quote from the literature,

“The difference occurs because Motorola presumes that the process mean can drift 1.5 sigma in either direction. The area of a normal distribution beyond 4.5 sigma from the mean is indeed 3.4 parts per million. Because control charts will easily detect any process shift of this magnitude in a single sample, the 3.4 parts per million represents a very conservative upper bound on the nonconformance rate."

So it’s still based on the fundamental assumption of normal distribution, with a little twist. Hope this helps tame your curiousity."