DPMO & Sigma Level
Defects per million opportunities, DPU, yield and sigma level from defects, units and opportunities (1.5σ shift shown separately), or DPMO from a sigma level.
DPU, DPO, DPMO, yield (and the Poisson estimate), short- and long-term sigma, a sigma-to-DPMO ladder, and notes on the shift convention and on counting opportunities.
Example: 34 defects in 10,000 units with 5 opportunities each: DPMO 680, yield 99.93 %, Z 3.20 long-term = 4.70 with the 1.5σ shift; six sigma with the shift is 3.4 DPMO.
Defects per million,
and the normal curve.
How DPMO is counted, how it becomes a sigma level, and what the 1.5σ shift is.
Counting
DPU = defects ÷ units; DPO = defects ÷ (units × opportunities per unit); DPMO = DPO × 10⁶. Yield is 1 − DPO (the share of opportunities without a defect); the Poisson estimate e^−DPU is the chance a unit has no defect at all. Opportunities are a definition — the more you count, the lower the DPMO for the same defects — so state them with the figure.
Sigma level
The sigma level is the normal-curve distance that leaves DPO in the tail: Z = Φ⁻¹(1 − DPO), computed with Acklam’s inverse-normal approximation and a refinement step. The Six Sigma convention adds 1.5σ for long-term drift, so "6σ" corresponds to 3.4 DPMO (Z = 4.5 without the shift). Both figures are shown; the shift is adjustable.
Reading it
Zero observed defects give no upper bound on quality — only a sample-size statement. The sigma level is a summary of a defect rate, not a capability index; Cp/Cpk from measurements are on the process-capability page. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- DPO = defects ÷ (units × opportunities); DPMO = DPO × 10⁶; Z = Φ⁻¹(1 − DPO) + shift; Φ⁻¹ by Acklam’s approximation with a refinement step; the 1.5σ shift is the Six Sigma convention, optional
Last reviewed 21 September 2026. How results are checked: How we verify.