Yes, thank you @Dr.Strangelove !
Okay way out of my depth here, and the whole thing seems like hooey, but I don’t think that’s where the argument breaks down, if I understand it anyway. A big if. …
The defective parts per million curve is still centered around the original origin. The bit is that the manufacturing process now shifts 1.5 SD in just one direction so one tail now sticks out beyond that, actually only 4.5 SD away, but the other is now 7.5 SD out and can be ignored.
I think.
Uh… maybe? I guess that’s as reasonable an explanation as any, even though it’s still nonsense. If you’re, say, drilling a hole, and there’s some upper and lower diameter tolerance, then when you tighten up the process you end up shrinking the number of defects on both sides. If that wasn’t the case, you’d want to recenter the target so that the number of defects is about the same in both directions. Arbitrarily moving the target to be 1.5 SD off makes no sense.
Oh I agree. I just think it’s not a math error more a basic assumptions pseudoscience error.
Maybe a math error in the sense of understanding significance? What’s a +/- for a made up assumption?
Given that a shift of 1.5 SD is something pulled out of the air (something about a stack of discs) rather than empirically observed, the language of mathematical precision used is silly.
Basically all it boils down to is saying that a process should aim for higher precision than is the actual goal to allow for messing up along the way that is unforeseen but unsurprising. Aim for the alliterative six sigma and you should end up with something decent.
Of course some defects are tolerable to have at higher rates and some outcomes must be thought of as aiming for being never events. A candy wrapper folded wrong can occur every so often but every EpiPen better work.
Math as marketing mumbo.
FWIW I just dug a little looking for any evidence that the 1.5 SD shift bit was anything other than a rough best guess stab and found this:
Bottom line is confirmation it was a best guess stab.