Statistical
Six Sigma DPMO and Rolled Throughput Yield (RTY) formulas
Calculate Defects Per Million Opportunities (DPMO) across multi-checkpoint units and chain step-by-step First Pass Yields with PRODUCT.
Defects vs Defective Units—and why RTY compounds with PRODUCT
A circuit board with 8 solder/test checkpoints presents 8 defect OPPORTUNITIES per unit. Inspecting 2,500 boards creates 2,500 * 8 = 20,000 opportunities; finding 68 defects yields DPMO = (68 / 20,000) * 1,000,000 = 3,400 DPMO.
Across multi-stage workflows (Step 1 FPY = 98%, Step 2 = 95%, Step 3 = 96%), probability of passing ALL steps without rework is Rolled Throughput Yield RTY = PRODUCT(D2:F2) = 89.38%—not AVERAGE(D2:F2) = 96.33%!
| Quality Metric | Formula | Result |
|---|---|---|
| Total Opportunities | 2,500 units * 8 opps/unit | 20,000 |
| DPMO (68 defects) | (68 / 20,000) * 1,000,000 | 3,400 DPMO |
| Opportunity Yield | 1 - (68 / 20,000) | 99.66% |
| 3-Step Rolled Yield (98%, 95%, 96%) | =PRODUCT(0.98, 0.95, 0.96) | 89.38% (0.8938) |
DPMO and Rolled Throughput Yield (RTY) formulas
Multiply UnitsInspected by OpportunitiesPerUnit in the denominator before scaling by 1,000,000.
=ROUND((C2 / (A2 * B2)) * 1000000, 1)Multi-step Rolled Throughput Yield (RTY)
Multiplies step-level First Pass Yields across D2:F2.
=ROUND(PRODUCT(D2:F2), 4)Inputs and interpretation
Define opportunities consistently across units and require positive inspected counts and opportunities. Defects are not the same as defective units. The opportunity-yield interpretation assumes each opportunity can be defective at most once. Multiplying conditional first-pass yields along one process path gives rolled yield; multiplying unrelated marginal rates requires additional independence assumptions. DPMO alone does not specify a sigma conversion convention.
Try the example
Use the original values or change them to test your understanding.