6σ is relatively new so I don't think people as old as audioguru will have learned it at college.
Yes, I vaguely remember touching on 6σ at college although we didn't study it in any great detail.
Statistics are not always helpful because there isn't always a Gaussian distribution centred around the typical values. For example I've measured 25 of a batch 5% tolerance resistors before and found the mean value was something like 1.03% below the rated value and no, this was not my meter's fault; it had been recently calibrated and had an accuracy of 0.1%. If you did a statistical calculation assuming a Gaussian distribution centred around the nominal value this would be nearly impossible.
So why did this happen? Could I have bought a duff batch?
No, none of the resistors were outside the tolerance band.
The answer is the consistency of the process must have been much better than 5%, probably closer to 2.5%. That way it doesn't matter if the process drifts slightly in either direction, it can be corrected every now and then. Heck I wouldn't even be surprised if there's some oscillation in the range of values produced.
marcbarker is probably right that most components are better than typical but it's always wise to at least assume slightly worse than typical values, especially when it's critical to the operation of the project.
How critical depends on the consequences of it going wrong.
If it's something non-critical such as battery life in a consumer product, then I'd use the typical values for say regulator drop-out because nothing bad is going to happen. However, if it was for a medical application were someone's life could be threatened if a certain component was off tolerance, I would go for worst case with an extra safety margin.