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DPMO to Sigma Level Converter
Turn defect counts into DPMO, sigma level, yield, and an equivalent Cpk in one pass. Start from raw counts, from a DPMO or PPM figure you already have, or run it backwards from a sigma level. Results use the standard 1.5 shift convention and match the published sigma tables.
How the math works
- DPMO = defects / (units × opportunities per unit) × 1,000,000. PPM defective is the same arithmetic with one opportunity per unit.
- Sigma level = invNorm(1 − DPMO / 1,000,000) + 1.5, the short-term convention with the standard 1.5 sigma shift.
- Yield % = (1 − DPMO / 1,000,000) × 100.
- Equivalent Cpk = (sigma level − 1.5) / 3. This is the long-term, convention-dependent figure: treat it as a translation, not a substitute for a real capability study.
- Reverse: DPMO = (1 − Φ(sigma level − 1.5)) × 1,000,000.
The inverse normal is computed directly (Acklam's algorithm) rather than stepped through a lookup table, so results are continuous and match the standard published sigma tables at every listed point.
Sigma level reference table
| Sigma level | DPMO | Yield |
|---|---|---|
| 1σ | 691,462 | 30.9% |
| 2σ | 308,538 | 69.1% |
| 3σ | 66,807 | 93.3% |
| 4σ | 6,210 | 99.38% |
| 5σ | 233 | 99.977% |
| 6σ | 3.4 | 99.99966% |
Worked example: invoice errors
A billing team audits 2,150 invoices, each checked for 4 error types (wrong amount, wrong customer, missing PO, wrong date), and finds 47 defects.
- DPMO = 47 / (2,150 × 4) × 1,000,000 = 5,465
- Sigma level = invNorm(1 − 0.005465) + 1.5 = 4.04
- Yield = 99.45%
- Equivalent Cpk = (4.04 − 1.5) / 3 ≈ 0.85
A process a touch above 4 sigma: far from crisis, far from finished. Hit "Load example" above to run these numbers through the converter.
FAQ
What is DPMO?
DPMO stands for defects per million opportunities. It normalizes defect data so processes of different complexity can be compared: DPMO = (defects / (units × opportunities per unit)) × 1,000,000. An opportunity is each independent chance for a defect on one unit, so an invoice checked for 4 error types has 4 opportunities.
How do you convert DPMO to a sigma level?
Convert DPMO to a defect probability (DPMO / 1,000,000), find the standard normal z-value for the complementary yield using the inverse normal function, then add the conventional 1.5 sigma shift: sigma level = invNorm(1 − DPMO/1,000,000) + 1.5. For example, 5,465 DPMO converts to roughly a 4.0 sigma level.
Why is there a 1.5 sigma shift in the conversion?
The 1.5 sigma shift is a Six Sigma convention that assumes a process mean drifts up to 1.5 sigma over the long term, even when short-term data looks centered. It is why 6 sigma corresponds to 3.4 DPMO instead of about 0.002 DPMO. It is a convention, not a law of nature, so always state whether a reported sigma level includes the shift.
What sigma level is a 99 percent yield?
A 99 percent yield means 10,000 DPMO, which converts to about a 3.83 sigma level using the standard 1.5 shift convention. It sounds impressive until you scale it: at 99 percent, a plant shipping 50,000 units a month sends out 500 defective ones.
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Counting defects is step one. Closing them is the system.
A sigma level tells you how often the process fails; a CAPA system is how you make each failure the last one. The OperationalPlaybook CAPA Quality System Templates give you the full corrective-action paper trail, editable and ready to use: investigation forms, root cause analysis, and effectiveness checks that turn this month's DPMO into next month's improvement.