Sigma Level Calculator — DPMO, Yield and Process Sigma
Turn defects, units and opportunities into DPU, DPMO, yield and process sigma, convert any sigma level to DPMO and back, and multiply step yields into rolled throughput yield. Both the 1.5-shifted and unshifted conventions, labelled.
From defect counts
Ways one unit can be defective that you actually check for.
First-pass yield of a whole unit, assuming defects fall at random (Poisson): 96.66 % = e−DPU. To see which defect types drive the count, put them on a Pareto chart; to watch the rate over time, a u chart.
Convert sigma level ↔ DPMO
Rolled throughput yield
Percentages or fractions, separated by commas: 98, 95, 99 or 0.98, 0.95, 0.99.
Sigma level to DPMO table
| Sigma level | DPMO | Yield | Equivalent Cpk | DPMO, no shift |
|---|---|---|---|---|
| 1.0 | 691,462 | 30.85375 % | 0.33 | 158,655 |
| 1.5 | 500,000 | 50.00000 % | 0.50 | 66,807 |
| 2.0 | 308,538 | 69.14625 % | 0.67 | 22,750 |
| 2.5 | 158,655 | 84.13447 % | 0.83 | 6,209.7 |
| 3.0 | 66,807 | 93.31928 % | 1.00 | 1,349.9 |
| 3.5 | 22,750 | 97.72499 % | 1.17 | 232.6 |
| 4.0 | 6,209.7 | 99.37903 % | 1.33 | 31.67 |
| 4.5 | 1,349.9 | 99.86501 % | 1.50 | 3.40 |
| 5.0 | 232.6 | 99.97674 % | 1.67 | 0.287 |
| 5.5 | 31.67 | 99.99683 % | 1.83 | 0.019 |
| 6.0 | 3.40 | 99.99966 % | 2.00 | 9.87e−4 |
DPMO = Φ(−(sigma − 1.5)) × 10⁶, one tail. The last column drops the shift: what a process whose nearer limit really is that many σ away would produce.
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The definitions
DPU (defects per unit) = defects ÷ units. DPO (defects per opportunity) = defects ÷ (units × opportunities per unit). DPMO = DPO × 1,000,000. Yield here is 1 − DPO, the fraction of opportunities that came out right.
The opportunity count is the number that most changes the answer and the one most worth arguing about. Count only the ways a unit can fail that a customer would notice and that you actually inspect for; inflating opportunities makes every process look like six sigma.
Why six sigma is 3.4 per million — the 1.5 shift
A process whose nearer limit is six standard deviations from a centred mean would make about two defects per billion. The 3.4 per million in every Six Sigma table comes from assuming the mean drifts 1.5σ toward a limit over the long term, so the tables look up Φ(−(σ − 1.5)).
This calculator prints both: the long-term Z (no shift, what your DPMO directly implies) and the short-term sigma level (Z + 1.5, the number in the tables). Quote the one your organisation uses, and say which.
Rolled throughput yield
First-pass yield at each step hides how much rework a line carries. Rolled throughput yield is the product of the step yields: three steps at 98 %, 95 % and 99 % pass only 92.2 % of units through every step right first time. Enter your step yields to see it.
Common questions
- How do I calculate DPMO?
- DPMO = defects ÷ (units × opportunities per unit) × 1,000,000. For example, 17 defects on 500 units with 4 opportunities each is 17 ÷ 2,000 × 1,000,000 = 8,500 DPMO.
- What sigma level is 3.4 DPMO?
- Six sigma, under the conventional 1.5σ long-term shift. Without the shift, 3.4 DPMO corresponds to a Z of 4.5.
- How do I convert a sigma level to Cpk?
- Divide the short-term sigma level by 3: a six-sigma process corresponds to a Cpk of 2.0 and a four-sigma process to 1.33. That holds for the nearer limit of a process with no long-term shift built in, so treat it as a rough equivalence.
- What is the difference between DPU and DPMO?
- DPU counts defects per unit and can exceed 1 when units carry several defects. DPMO normalises by the number of opportunities for a defect, so products of different complexity can be compared on the same scale.