Six Sigma DPMO Calculator
Calculate Defects Per Million Opportunities (DPMO), Sigma Level, and Process Yield to measure and improve process quality using Six Sigma methodology.
Formulas Used
DPO (Defects Per Opportunity):
DPO = Defects ÷ (Units × Opportunities per Unit)
DPMO (Defects Per Million Opportunities):
DPMO = DPO × 1,000,000
Process Yield:
Yield (%) = (1 − DPO) × 100
Sigma Level (with 1.5σ long-term shift):
Sigma Level = NORMSINV(1 − DPO) + 1.5
where NORMSINV is the inverse of the standard normal cumulative distribution function.
Sigma Benchmarks (with 1.5σ shift):
| Sigma Level | DPMO | Yield |
|---|---|---|
| 6σ | 3.4 | 99.99966% |
| 5σ | 233 | 99.977% |
| 4σ | 6,210 | 99.379% |
| 3σ | 66,807 | 93.319% |
| 2σ | 308,537 | 69.146% |
Assumptions & References
- The 1.5 sigma shift is applied per the Motorola/industry standard to account for long-term process drift. Short-term sigma = NORMSINV(1 − DPO); long-term sigma adds 1.5.
- All defect opportunities within a unit are assumed to be independent and equally likely.
- The inverse normal CDF is approximated using the Abramowitz & Stegun rational approximation (maximum error < 1.5 × 10⁻⁵).
- Sigma level is capped at 6.0σ for display purposes when zero defects are observed.
- This calculator measures attribute data (defective/non-defective). Variable data requires a different approach (process capability indices Cp, Cpk).
- References: Motorola University (1986) — Six Sigma origin; Montgomery, D.C. — Introduction to Statistical Quality Control; ASQ Six Sigma Body of Knowledge.