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DPMO and sigma level calculator
Enter the defects you found, the units you inspected and the opportunities for a defect on each unit. You get DPU, DPO, DPMO, yield and the process sigma level.
How it is calculated
The sigma level is the z-score whose upper-tail area equals the defect rate, plus 1.5. The 1.5σ is a Six Sigma convention for long-term drift between subgroups: data collected over months usually looks worse than a short study. Some companies report the long-term Z without the shift, so always say which one you mean.
Sigma level table
| Sigma level (with 1.5σ shift) | DPMO | Yield |
|---|---|---|
| 1σ | 691,462 | 30.9% |
| 2σ | 308,538 | 69.1% |
| 3σ | 66,807 | 93.3% |
| 4σ | 6,210 | 99.379% |
| 4.5σ | 1,350 | 99.865% |
| 5σ | 233 | 99.97674% |
| 6σ | 3.4 | 99.99966% |
Computed from the normal distribution with the 1.5σ shift, one tail. 6σ is 3.4 DPMO.
Mistakes to avoid
- Counting defectives as defects. If a unit can only pass or fail, opportunities per unit is 1.
- Padding opportunities. More opportunities give a smaller DPMO for the same process. Define them once and keep them.
- Treating sigma level as capability. Sigma level comes from counted defects. Cpk comes from measured data and spec limits. Use the process capability calculator for that.
Read more: Sigma level and DPMO guide · Binomial vs Poisson · Process capability (Green Belt)
FAQ
What is a good DPMO?
It depends on the process and the cost of a defect. As a rough scale (with the 1.5σ shift), 66,807 DPMO is 3 sigma, 6,210 is 4 sigma, 233 is 5 sigma and 3.4 is 6 sigma. Compare a process with its own history and with what the customer needs, not with a slogan.
Is six sigma really 3.4 defects per million?
Only with the conventional 1.5σ long-term shift. A process whose nearest spec limit sits 6 standard deviations from the mean, with no shift at all, produces about 0.001 DPMO per side. 3.4 DPMO is the upper tail at 4.5σ, which is 6σ minus the 1.5σ shift.
What is the difference between DPU and DPMO?
DPU (defects per unit) is defects divided by units. DPMO divides by the number of opportunities as well, then multiplies by a million, so products of different complexity can be compared. A board with 500 solder joints has more chances to fail than a bracket with 2 holes.
Defects or defectives: which do I count?
DPMO counts defects (individual flaws), and one unit can have several. If you only know how many units failed (defectives), set opportunities per unit to 1; DPMO then equals the defective rate in parts per million.
How do I choose the number of opportunities per unit?
Count only the things that can independently go wrong, that the customer cares about and that you actually check. Inflating opportunities makes the sigma level look better without changing the process, so write the definition down and keep it fixed.
This shows up on the exams as a calculation question. Practice it with new numbers every time, and every wrong answer explained.
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