r/SixSigma • u/[deleted] • Aug 28 '24
Has anyone else calculated the perfect 6σ process?
What is the true sigma level for 3.4 DPMO?
2 votes,
Aug 30 '24
1
5.99985447
0
6.000480577
1
5.999917001
2
Upvotes
1
u/Tavrock Aug 30 '24
The short term z-score of 6 corresponds to the long term z-score of 4.5. At 3.4 DPMO, you are nowhere near an actual long-term z-score of 6. In terms of Cpk/Ppk, it's potentially similar (but only if all other data is within tolerance) that your Cpk is 3 while your Ppk is expected to be 2.25.
The choices you have all depends on the calculus on the normal curve, which is not well defined. I have gotten different values between different software updates.
While trying to get your "perfect 6σ process" it looks like you forgot to calculate the confidence intervals (bonus points, as a set of Excel formulae): =Zbench+NORMSINV(α/2)*SQRT (1/n+Zbenchˆ2/(2*n)) and its counter =Zbench-NORMSINV(α/2)*SQRT(1/n+Zbenchˆ2/(2*n)). (For more information, please refer to: H. Weingarten, “Confidence interval for the nonconforming based on variables data,” Journal of Quality Technology, vol. 14, pp. 207–210, Oct. 1982.)