When Six Sigma people talk "six sigma processes," what they mean is that they want to have processes where there are (at least) six standard deviations between the mean and acceptance limit. For example, a factory that makes airline grade aluminum with mean tensile strength of 65 ksi, the lower acceptance limit 64 ksi, and standard deviation 0.167 ksi is Six Sigma. Six Sigma accounts for a possible 1.5-sigma shift of the mean.

Incorporating a shift of the mean of 1.5 standard deviations, there will be about =1000000*(1-NORM.DIST(6, 1.5, 1, 1)) = 3.4 defects per million.

In the case of the tensile strength of airline grade aluminum, Six Sigma's is likely a good level to be at because catastrophic failure on an airplane could open lawsuits costing billions of dollars. However, other processes likely don't need to be Six Sigma.

1. Give an example from your own manufacturing or business life of random processes that are likely to be normally distributed.
2. Describe the lower or upper acceptance limit of this process?
3. What should the sigma level be, or how many standard deviations should there be between the mean of the process and the limit?
4. Assuming a 1.5-sigma shift in the mean and assuming a one-sided acceptance limit, what should your reject rate be?

¹Six Sigma - Wikipedia