DPMO – defects per million opportunities – is the yardstick of Six Sigma quality programmes. Counting defects per unit is unfair when products differ in complexity: a pair of jeans has a handful of things that can go wrong, a circuit board hundreds. DPMO divides the defects by the number of opportunities for a defect, so simple and complex processes can be compared on one scale.
Enter how many defects you found, how many units you inspected and how many distinct defect opportunities each unit has. The calculator gives the DPMO, the defects per unit, the yield (share of opportunities without a defect) and the sigma level. By convention the sigma level adds a 1.5σ shift to allow for long-term drift of the process mean, which is why “six sigma” corresponds to 3.4 DPMO rather than about 0.001. You can switch the shift off to get the short-term (unshifted) value.
As a rule of thumb, 3σ (66,807 DPMO) is typical of average industry, 4σ (6,210) of good processes, 5σ (233) of very good ones, and 6σ (3.4) is world class.
How to use the DPMO Calculator
- Number of defects
- Number of units inspected
- Defect opportunities per unit
- Sigma convention
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
DPMO is defects divided by total opportunities, times one million. The sigma level is the z-value of the normal distribution whose upper tail equals the DPO, plus the 1.5σ shift.
Worked example
A jeans factory inspects 10,000 pairs with 5 defect opportunities each and finds 11 defects: DPO = 11 ÷ 50,000 = 0.00022, so DPMO = 220 and DPU = 0.0011. The yield is 99.978%, and Φ⁻¹(0.99978) = 3.51, giving a sigma level of 3.51 + 1.5 = 5.01σ. An office finding 17 errors in 20,000 spreadsheets with 75 cells to check each has DPMO = 17 ÷ 1,500,000 × 10⁶ = 11.33 and a sigma level of about 5.74.
Sigma level table (1.5σ shift)
| Sigma | DPMO | Yield |
|---|---|---|
| 2σ | 308,538 | 69.1% |
| 3σ | 66,807 | 93.3% |
| 4σ | 6,210 | 99.38% |
| 5σ | 233 | 99.977% |
| 6σ | 3.4 | 99.99966% |
Tips
- Measure the longest points of the package, including bulges.
- Check your carrier’s current divisor and rounding rules.
- Every field has a unit menu – cm, inches, kg and lb all work.
- Everything is calculated in your browser.
Common mistakes to avoid
- Using the wrong dimensional divisor for the carrier or service.
- Forgetting pallet height and overhang limits.
- Rounding dimensions down instead of up.
Inputs explained
| Field | What to enter |
|---|---|
| Number of defects | A number |
| Number of units inspected | A number |
| Defect opportunities per unit | A number |
| Sigma convention | Choose one: With 1.5σ shift (Six Sigma tables), No shift (short-term) |
What each result means
- DPO = [Number of defects]÷([Number of units inspected]×[Defect opportunities per unit])
- Defects per million opportunities (DPMO) = [Number of defects]÷([Number of units inspected]×[Defect opportunities per unit])×1e6
- Defects per unit (DPU) = [Number of defects]÷[Number of units inspected]
- Defects per million units = [Number of defects]÷[Number of units inspected]×1e6
- Yield (opportunities without defect) = (1 – [Number of defects]÷([Number of units inspected]×[Defect opportunities per unit]))×100
- First-pass yield estimate (e^−DPU) = (exp(-[Number of defects]÷[Number of units inspected]))×100
Formula
DPO = defects ÷ (units × opportunities) · DPMO = DPO × 1,000,000 · DPU = defects ÷ units · Yield = 1 − DPO · Sigma level = Φ⁻¹(1 − DPO) + 1.5
Worked example
Inputs — Number of defects: 11; Number of units inspected: 10,000; Defect opportunities per unit: 5; Sigma convention: With 1.5σ shift (Six Sigma tables).
Results — DPO = 0.00022; Defects per million opportunities (DPMO) = 220; Defects per unit (DPU) = 0.0011; Defects per million units = 1,100; Yield (opportunities without defect) = 99.978 %; First-pass yield estimate (e^−DPU) = 99.89 %; Sigma level = 5.01; Quality rating = Very good (5σ – 6σ).
Key terms
- DPO
- Defects per opportunity.
- Defect opportunity
- A measurable characteristic that could be defective.
- Sigma level
- Process capability expressed in standard deviations.
- 1.5σ shift
- Allowance for long-term drift used in Six Sigma tables.
Frequently asked questions
What is DPMO?
Defects per million opportunities: defects ÷ (units × opportunities per unit) × 1,000,000.
How many DPMO is Six Sigma?
3.4 DPMO with the conventional 1.5σ shift.
What is the difference between DPMO and PPM?
PPM counts defective units per million units; DPMO counts defects per million opportunities, so it accounts for complexity.
Why add 1.5 to the sigma level?
Six Sigma assumes the process mean drifts by about 1.5σ in the long term, so short-term performance is stated 1.5σ higher.
What is a defect opportunity?
A distinct, measurable way a unit can fail to meet requirements – define them before counting.
What sigma level is 220 DPMO?
About 5.01σ with the 1.5σ shift.
How do I improve my sigma level?
Reduce defects with root-cause analysis (DMAIC), mistake-proofing and process control.