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DPMO and sigma level calculator
DPMO, defects per million opportunities, is the number of defects a process would make in a million chances to make one. It is defects ÷ (units × opportunities per unit) × 1,000,000. The sigma level restates DPMO on the Six Sigma scale, where 6 sigma is 3.4 DPMO and 3 sigma is about 66,800.
DPUequalsDefects divided by Units
DPMOequalsDefects divided by Units × Opportunities per unit × 1,000,000
Sigma levelequalsz value of (1 − DPMO ÷ 1,000,000) + 1.5
Count every defect; one unit can have several
Units checked in the same period
Distinct ways a unit can fail that you check for
Pre-filled with the worked example. The sigma level includes the usual 1.5 sigma shift, the convention behind Six Sigma tables.
Sigma level
4.08
5,000 defects per million opportunities.
DPMO
5,000
Defects ÷ (units × opportunities) × 1,000,000
Yield
99.500%
Opportunities without a defect
Defects per unit (DPU)
0.05
Defects ÷ units
Sigma without the shift
2.58
Long-term z value of the yield
How to calculate it
Three counts from your inspection data
Defects are every nonconformity found, so a unit with two faults adds two. A defect check sheet is the simplest way to collect the count by type.
Units are the units inspected in the same period, good and bad.
Opportunities per unit are the distinct characteristics you check that could each be wrong. Keep the list short and fixed: padding it with features that never fail makes the sigma level look better than the process is.
Use DPMO and sigma level to compare processes or products of different complexity, and to track one process before and after a DMAIC project. For a single measured characteristic against its specification limits, Cp and Cpk say more, and for how many units get through each step without rework, use first pass yield.
Worked example
Illustrative numbers, not a benchmarkAn inspection of 500 circuit boards, each checked for 10 kinds of defect, finds 25 defects in total.
- 1Opportunities = 500 units × 10 = 5,000.
- 2DPU = 25 ÷ 500 = 0.05 defects per unit.
- 3DPMO = 25 ÷ 5,000 × 1,000,000 = 5,000.
- 4Yield = 1 − 5,000 ÷ 1,000,000 = 99.5%.
- 5Sigma level = NORM.S.INV(0.995) + 1.5 = 2.576 + 1.5 = 4.08.
Sigma level to DPMO table
| Sigma level | DPMO | Yield |
|---|---|---|
| 1 | 691,462 | 30.9% |
| 2 | 308,538 | 69.1% |
| 3 | 66,807 | 93.3% |
| 4 | 6,210 | 99.38% |
| 5 | 233 | 99.977% |
| 6 | 3.4 | 99.99966% |
Worked out with the 1.5 sigma shift, the same convention the calculator uses. The shift goes back to Motorola, where Six Sigma started, and is a convention rather than a measured fact about your process; the Wikipedia article on Six Sigma covers the debate. Whichever you use, use it every time.
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<p style="font:13px/1.4 sans-serif"><a href="https://www.theleansuite.com/tools/dpmo-calculator">DPMO and sigma level calculator</a> by LeanSuite</p>How LeanSuite helps
LeanSuite's Quality Improvement tools log quality issues from the floor, trace each one to its root cause and follow the corrective action through to closure, with custom KPIs that show where defects happen.
See Quality ImprovementRead more
- Free template: Defect check sheet
- Six Sigma in the lean glossary
- What is the Six Sigma Lean Methodology?
- Parts per million (PPM) in the lean glossary
- Defects per hundred units in the lean glossary
- Lean Six Sigma Tools: 13 Common Tools and When to Use Them
- DMAIC Process: The 5 Phases of Six Sigma, With Examples
FAQ
DPMO and sigma level calculator: common questions
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