Sigma level and DPMO calculator
Enter defects, units and error opportunities per unit: it gives you the defects per million (DPMO), the yield and the sigma level.
DPMO
5,000
Yield
99.500%
Sigma level
4.08
DPMO = defects ÷ (units × opportunities) × 1,000,000. The sigma level includes the 1.5 shift of the Six Sigma convention. The preloaded values are the letters-with-errors example from the Council for Six Sigma Certification (150,000 opportunities, 750 defects): between 4.0 and 4.1 sigma.
How it works
You enter the defects found, the units inspected and the error opportunities per unit.
- DPMO = defects ÷ (units × opportunities per unit) × 1,000,000.
- Yield = 100% − DPMO ÷ 10,000, the percentage without defects.
- Sigma level = inverse of the normal distribution applied to the yield + 1.5. The 1.5 is the long-term shift of the Six Sigma convention; it is the same calculation as NORM.S.INV(1 − DPMO ÷ 1,000,000) + 1.5 in Excel.
With this convention, 3.4 DPMO corresponds to 6 sigma and 66,807 DPMO to 3 sigma, values that match the Six Sigma Council table. With no defects there is no sigma level to calculate. The most delicate part is defining what counts as an "error opportunity": with more opportunities per unit the DPMO goes down, so the same criterion must be used when comparing before and after.
Sources
These are the ones from the article where the theory behind this tool is developed.
What does each level mean and where does the 3.4 come from? It is in the article Six Sigma: what it is, what the sigma level means and how it is calculated.