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This topic contains 5 replies, has 6 voices, and was last updated by Joe BB 9 years, 9 months ago.
I have 2 inquiries:
1. In the formulas for Cp and Cpk, where did the 6 (denominator – Cp formula) come from? where did the 3 (denominator – Cpk) come from? Can somebody please send me a derivation?
2. Why 6 sigma? why not 7 sigma, 8 sigma, etc.? what is the significance of 6 sigma? (statistically?)
I hope i will get clarifications regarding my stupid(?) questions. I just need to fully understand these.
Thank you very much!
The 6 of the Cp and the 3 of the Cpk comes from the fact that virtually all the individuals of the normal distribution fall within ±3 sigmas from the average. However, this is arbritary. What is “virtually all? 99.73% if we take ±3 sigmas. However, it is not allways like this. Whith the quality improving, the % of non conforming turned to PPM (parts per million), and wat was “virtually all good” (99.73%) bacame 2700 PPM, a figure not acceptable in many cases. 6 sigmas is the new “virtually all”. It means that the closest specification limit should be at least 6 sigmas away from the average. That is a Cpk>2, and it is 0.0something PPM or, if you accept that the process mean will drift 1.5 sigmas (Cpk>1.5) it is only 3.4 PPM. On the other hand, some times (for example when evaluating the measurement uncertainty) “virtually all” becames ±2 sigmas, containing about the 95% of the population.
As you see, even when there is a conceptual background, the final figure is arbitrary. It’s like asking why is the speed limit 55 MPH, and not 50 or 60? The faster you go, there are grater chances to have an accident and also, given the accident, to get seriously injured in it. But there is no “physical limit” in the 55 after all. People have left uninjured from a crash at 100 MPH, and others got killed at 30 MPH.
Six Sigma is also the name of a discipline, but in this context it is just a name, like TQM or Global 8D.
Gabriel,
That was no answer at all. I have the same question. Instead of the usual marketingbabble, why not say what the error rates are at weach sigma level. Geez
Well, Duh,A very appropriate name for … You are responding to Gabriel’s post from 2002.
SOS, just a different year. You are right, I look here every other day or so but don’t have a desire to take on the ignorance.
As ignorant and arrogant as ever!
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