Enter how many units you inspected, how many defect opportunities each unit has and how many defects you found. The calculator returns DPU, DPO, DPMO, first-pass yield, PPM defective and the process sigma level, with and without the conventional 1.5σ shift.
DPMO (defects per million opportunities) counts defects against every chance a unit had to be wrong, scaled to one million; with photo-evidence QC software such as AutoQC, the counts come from a per-piece record rather than a tally sheet. Because it divides by opportunities, it lets you compare a simple part with a complex assembly on one scale. The sigma level converts the same defect rate into a position on the standard normal curve: the higher the sigma, the fewer defects per million. Quality teams use the pair to track a line or a supplier over time, to compare partners making different products, and to set an improvement target that everyone reads the same way.
| Measure | Formula |
|---|---|
| DPU | Defects ÷ units inspected |
| DPO | Defects ÷ (units × opportunities per unit) |
| DPMO | DPO × 1,000,000 |
| First-pass yield | (Units − defective units) ÷ units × 100; if defective units are blank, estimated as e−DPU × 100 (Poisson) |
| PPM defective | Defective units ÷ units × 1,000,000 |
| Sigma level, no shift | NORMSINV(1 − DPO) |
| Sigma level, 1.5σ shift | NORMSINV(1 − DPO) + 1.5 |
NORMSINV is the inverse of the standard normal distribution (the same function as NORM.S.INV in a spreadsheet). The calculator computes it in your browser with Peter Acklam’s rational approximation, which is accurate to about nine significant digits across the range used here.
The 1.5σ shift is a Six Sigma convention: it assumes a process drifts by about 1.5 standard deviations over the long run, so a short-term sigma is reported as the long-term figure plus 1.5. That is why 3.4 DPMO is called “six sigma” even though NORMSINV(1 − 0.0000034) is about 4.5. Both figures are shown so you can quote whichever your organisation uses; always say which one you quote.
A brand checks 1,000 restaurant table tops made by an OEM partner. Each top has five opportunities: length, width, thickness, edge finish and the label. Inspectors log 38 defects spread across 30 tops.
These are example numbers, not a benchmark. Notice that PPM defective (30,000) is much larger than DPMO (7,600): one counts bad units, the other spreads defects across five opportunities per unit.
| Sigma level | DPMO | Yield per opportunity |
|---|---|---|
| 2σ | 308,538 | 69.1% |
| 3σ | 66,807 | 93.3% |
| 4σ | 6,210 | 99.38% |
| 5σ | 233 | 99.977% |
| 6σ | 3.4 | 99.99966% |
A sigma figure is only as good as the defect counts behind it. In AutoQC, each piece gets its own barcode, its four photos are checked against the SKU spec and its tolerance, and brand QA passes, redoes or holds it with a reason, so every unit, defect and defective piece you enter here traces back to that piece’s photos and QA decision. The checks that feed those counts at the partner’s line are listed in the pre-dispatch inspection checklist.
Divide the number of defects by the number of units inspected multiplied by the opportunities per unit, then multiply by 1,000,000. For 38 defects in 1,000 units with 5 opportunities each, DPMO is 38 ÷ 5,000 × 1,000,000 = 7,600.
Take DPO (DPMO ÷ 1,000,000) and compute NORMSINV(1 − DPO), or NORM.S.INV in a spreadsheet. That is the sigma level without shift; add 1.5 for the conventional short-term Six Sigma figure.
Because of the 1.5σ shift convention. NORMSINV(1 − 0.0000034) is about 4.5; adding the assumed 1.5σ long-term drift gives 6.0.
DPMO counts defects per million opportunities, so one unit can contribute several. PPM defective counts defective units per million units, regardless of how many defects each has.
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