About this calculator
DPMO (defects per million opportunities) compares quality across products of different complexity, because it counts every way a unit could fail. The sigma level turns DPMO into a single score: the higher, the better. By the usual Six Sigma convention, 3σ ≈ 66 807 DPMO, 4σ ≈ 6210, 5σ ≈ 233 and 6σ ≈ 3.4 DPMO.
Formula
DPO = Defects ÷ (Units × Opportunities) DPMO = DPO × 1 000 000
Sigma level = Φ⁻¹(1 − DPO) + 1.5
Φ⁻¹ is the inverse of the standard normal distribution. The 1.5 is the conventional allowance for long-term process drift used in Six Sigma tables. DPU = Defects ÷ Units.
Worked example
1000 units, 5 opportunities each, 10 defects found:
- DPO = 10 ÷ 5000 = 0.002 → DPMO = 2000
- DPU = 10 ÷ 1000 = 0.01
- Φ⁻¹(0.998) = 2.878, so sigma level = 2.878 + 1.5 = 4.38σ
Assumptions and limitations
- Opportunities must be defined consistently. Counting extra trivial opportunities makes DPMO look better without any real improvement.
- The 1.5σ shift is a convention, not a measured property of your process.
- Results from small samples are uncertain; inspect enough units for a meaningful figure.
References
- Six Sigma DPMO and sigma-level conversion (Motorola convention with 1.5σ shift).