Sigma level and DPMO
DPMO (Defects Per Million Opportunities) is the standard metric for Six Sigma process capability. It counts defects relative to the total number of chances for a defect to occur.
The sigma level corresponding to a DPMO uses the standard normal distribution plus a 1.5σ shift that accounts for long-term process drift (the “Motorola shift”). At 6σ: DPMO = 3.4.
Worked example
A call centre handles 5,000 calls. Inspectors find 200 calls with one or more errors. Each call has 1 opportunity for an error.
DPMO benchmarks
| Sigma level | DPMO | Yield |
|---|---|---|
| 3σ | 66,807 | 93.32 % |
| 4σ | 6,210 | 99.38 % |
| 5σ | 233 | 99.977 % |
| 6σ | 3.4 | 99.99966 % |
Multiple opportunities per unit
Example: 100 invoices inspected, 8 defects found, 5 opportunities per invoice.
Working from a measured characteristic instead of counted defects? The free process capability calculator turns spec limits, mean and σ into Cpk, Ppk and expected PPM.
Common exam traps
- The 1.5σ shift is always applied in Six Sigma DPMO tables. The short-term z for 6σ is 6.0 (0.001 PPB), but the published DPMO = 3.4 uses z = 4.5 (6 − 1.5). Exam problems that say “sigma level” typically use the shifted table.
- Defining opportunities consistently. The sigma level depends heavily on how many opportunities you count. More (reasonable) opportunities per unit gives a lower DPMO for the same defect count—which can look like better performance without any real improvement.
- DPO is not the same as defect rate. A unit can have multiple defects, each using a separate opportunity.
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