Adonis Tools
Sigma Level and Defect Rate Calculator
Calculate Sigma Level, DPMO, DPU, DPO, and process yield using Six Sigma methodology, for discrete defect counts or continuous measurement data.
Discrete Data Inputs
Use this mode for attribute / pass-fail data — counted defects across inspected units, such as defects on a form, an assembly, or a transaction.
Total number of units, parts, or transactions checked
Distinct ways a defect could occur on one unit
Count of all defects observed across all units
Results
Based on the discrete data entered above.
Continuous Data Inputs
Use this mode for variable / measured data against upper and lower specification limits, such as a dimension, weight, or fill volume.
Results
Based on the continuous data entered above.
Formulas & Methodology Reference
Discrete (Attribute) Data
DPU = Defects ÷ Units
DPO = Defects ÷ (Units × Opportunities per unit)
DPMO = DPO × 1,000,000
Yield (Poisson) = e⁻ᴰᴾᵁ × 100%
Yield (Direct) = (1 − DPO) × 100%
Sigma Level = Φ⁻¹(1 − DPO) + 1.5 (shift optional)
Continuous (Variable) Data
Z(USL) = (USL − mean) ÷ σ
Z(LSL) = (mean − LSL) ÷ σ
p(defect) = P(X > USL) + P(X < LSL), from the standard normal distribution
DPMO = p(defect) × 1,000,000
Yield = (1 − p(defect)) × 100%
Z.Bench = Φ⁻¹(1 − p(defect))
Sigma Level = Z.Bench + 1.5 (shift optional)
Cp = (USL − LSL) ÷ 6σ · Cpk = min[(USL−mean), (mean−LSL)] ÷ 3σ
Cp and Cpk are short-term capability indices, appropriate when the standard deviation entered reflects short-term (within-subgroup) variation. This calculator does not compute Pp/Ppk, which require an overall (long-term) standard deviation typically estimated from subgrouped data collected over time.
The 1.5σ Shift
Six Sigma methodology conventionally assumes a process mean drifts by about 1.5σ over the long run relative to short-term data. Toggling the shift off reports the short-term (instantaneous) sigma level; toggling it on reports the commonly-quoted long-term sigma level, for example "Six Sigma" as 3.4 DPMO corresponds to a 4.5σ short-term process plus the 1.5σ shift.
Sigma Level Quality Reference
| Sigma Level | Approx. DPMO | Rating |
|---|---|---|
| 1σ | ~ 690,000 | Non-Competitive |
| 2σ | ~ 308,000 | Needs Improvement |
| 3σ | ~ 66,800 | Below Average |
| 4σ | ~ 6,210 | Industry Average |
| 5σ | ~ 230 | Excellent |
| 6σ | ~ 3.4 | World Class |
DPMO figures assume the standard 1.5σ long-term shift. All calculations use the standard normal distribution as an approximation; real-world processes may deviate from normality.
For educational purposes only. Not intended for regulated quality, safety, or compliance decisions.