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Cpk to ppm and sigma converter
Convert in any direction. Assumes a normal, stable process.
Cpk to ppm table
| Cpk | z = 3·Cpk | ppm, nearest side | ppm, centered (both sides) | ppm with 1.5σ shift |
|---|---|---|---|---|
| 0.33 | 0.99 | 161,087 | 322,174 | 694,974 |
| 0.50 | 1.50 | 66,807 | 133,614 | 500,000 |
| 0.67 | 2.01 | 22,216 | 44,431 | 305,026 |
| 0.83 | 2.49 | 6,387 | 12,774 | 161,087 |
| 1.00 | 3.00 | 1,350 | 2,700 | 66,807 |
| 1.10 | 3.30 | 483 | 967 | 35,930 |
| 1.20 | 3.60 | 159 | 318 | 17,864 |
| 1.33 | 3.99 | 33.04 | 66.07 | 6,387 |
| 1.50 | 4.50 | 3.40 | 6.80 | 1,350 |
| 1.67 | 5.01 | 0.272 | 0.544 | 224 |
| 1.83 | 5.49 | 0.020 | 0.040 | 33.04 |
| 2.00 | 6.00 | 9.9e-4 | 0.002 | 3.40 |
ppm = 10⁶ × P(Z > 3·Cpk). The last column subtracts the conventional 1.5σ long-term shift: 10⁶ × P(Z > 3·Cpk − 1.5).
Read more: Cp, Cpk and Cpm · Cpk vs Ppk · Sigma level and DPMO
FAQ
How many ppm is a Cpk of 1.33?
About 33 ppm beyond the nearest spec limit (z = 3.99). If the process is centered, the other side adds the same again, about 66 ppm in total. These figures assume a normal, stable process.
Why does Cpk 1.5 equal six sigma?
Six Sigma's convention allows the mean to drift 1.5σ in the long term. A short-term Cpk of 2.0 (z = 6) shifted by 1.5σ leaves 4.5σ to the limit, which is 3.4 ppm. A long-term Ppk of 1.5 (z = 4.5) gives the same 3.4 ppm directly.
Is ppm from Cpk accurate?
Only as accurate as the normal assumption, and only in the tail you are predicting. Skewed data can make a ppm estimate wrong by orders of magnitude. Check normality first and, where possible, compare with actual defect counts.
One-sided or two-sided ppm?
Cpk describes only the nearer spec limit, so the one-sided figure is the minimum defect rate. For a centered process (Cp = Cpk), double it. For an off-center process, compute each side with the process capability calculator.
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