DPMO and sigma level calculator
Convert defect counts into defects per million opportunities (DPMO), process yield and a Six Sigma level.
Track defects over time
Need to follow this process after the one-off calculation? The SPC X-bar and R Control Chart Template helps you monitor defects with control charts.
How it is calculated
DPMO = defects ÷ (units × opportunities per unit) × 1,000,000. Yield = 1 − DPMO ÷ 1,000,000. Sigma level = Φ⁻¹(yield) + 1.5, where Φ⁻¹ is the inverse standard normal and 1.5 is the conventional long-term shift.
Worked example
25 defects, 1000 units, 5 opportunities: DPMO = 25 ÷ 5000 × 10⁶ = 5,000, yield 99.5 %, sigma = 2.576 + 1.5 = 4.08.
Steps
- Count defects and units from the inspection log.
- Count the defect opportunities on one unit, and enter that number.
- Read DPMO, yield and sigma level.
Frequently asked questions
Why add 1.5 to the sigma level?
It is the Motorola convention for long-term drift of the process mean. Short-term sigma is the value without the shift.
What is a six sigma process?
About 3.4 DPMO with the 1.5 shift. Many processes run at 3 to 4 sigma.
What if I have no defects?
Sigma is undefined at zero DPMO. Use a larger sample or report the limit.
Related calculators
References
DPMO and sigma conversion per Harry and Schroeder, Six Sigma, and the standard normal inverse. Inverse normal by Acklam approximation.
Estimates for information only. Verify critical values with a qualified engineer or your supplier standards.