Quality & Statistics
DPMO / Sigma Level Calculator
Defects per million opportunities, DPU, DPO, yield, and the corresponding Six Sigma process level.
DPMO = D ÷ (U × O) × 10⁶What is DPMO?
DPMO (Defects Per Million Opportunities) normalizes defect rates across different products and processes by accounting for the number of opportunities for a defect in each unit. It enables fair comparison between a simple product with 2 features and a complex one with 200.
Defects per million opportunities
DPMO = Defects ÷ (Units × Opportunities) × 10⁶Key metrics
| Metric | Definition |
|---|---|
| DPU | Defects per unit = total defects ÷ total units |
| DPO | Defects per opportunity = defects ÷ (units × opportunities) |
| DPMO | DPO × 1,000,000 |
| Yield | (1 − DPO) × 100% |
| Sigma level | Z-score corresponding to the yield, plus the 1.5σ shift |
Six Sigma reference table
| Sigma level | DPMO | Yield | Defect rate |
|---|---|---|---|
| 1σ | 691,462 | 30.85% | 69.15% |
| 2σ | 308,538 | 69.15% | 30.85% |
| 3σ | 66,807 | 93.32% | 6.68% |
| 4σ | 6,210 | 99.38% | 0.62% |
| 5σ | 233 | 99.977% | 0.023% |
| 6σ | 3.4 | 99.99966% | 0.00034% |
Values include the conventional 1.5σ long-term shift.
Frequently asked questions
What is the 1.5 sigma shift?
Motorola’s Six Sigma methodology accounts for a 1.5σ long-term shift in process mean. A “6 sigma” process has 3.4 DPMO, which corresponds to 4.5σ on a standard normal distribution plus the 1.5σ shift allowance.
How do I identify opportunities per unit?
An opportunity is any measurable characteristic that could potentially be defective. For a welded assembly with 10 welds, there are 10 opportunities per unit (assuming each weld could independently fail).