Defect Rate Calculator
Calculate defect rate, defects per million opportunities (DPMO), yield, and Sigma level to measure and monitor process quality.
Number of ways a unit can be defective (default: 1)
Formulas Used
Defect Rate:
Defect Rate = Defective Units ÷ Total Units Produced
Yield:
Yield = 1 − Defect Rate
Defects Per Opportunity (DPO):
DPO = Defective Units ÷ (Total Units × Opportunities per Unit)
Defects Per Million Opportunities (DPMO):
DPMO = DPO × 1,000,000
Rolled Throughput Yield (RTY):
RTY = (1 − DPO)Opportunities per Unit
Sigma Level (approximation):
σ ≈ 0.8406 + √(29.37 − 2.221 × ln(DPMO))
Valid for DPMO between 3.4 and ~933,000 (1σ to 6σ)
Assumptions & References
- A defective unit is any unit that fails to meet specifications, regardless of the number of defects it contains.
- Opportunities per unit refers to the number of distinct ways a single unit can be found defective (e.g., a circuit board with 5 solder joints has 5 opportunities).
- The Sigma Level approximation uses the Bothe (1997) formula and is accurate to within ±0.03σ for DPMO values between 3.4 and 933,193.
- Six Sigma quality corresponds to 3.4 DPMO, assuming a 1.5σ long-term process shift (Motorola convention).
- Rolled Throughput Yield (RTY) assumes defects at each opportunity are independent and identically distributed.
- This calculator measures unit-level defects. For defect-count-based analysis (e.g., defects per unit, DPU), use a separate DPU/Poisson model.
- References: Montgomery, D.C. (2020). Introduction to Statistical Quality Control, 8th ed.; iSixSigma DPMO & Sigma Level tables.