Cpk calculator (Cp, Cpk, Pp, Ppk and PPM)
Enter the specification limits, the process mean and the standard deviation. Use σ within (short-term, e.g. R̄/d₂ from a control chart) for Cp and Cpk, or σ overall (the sample standard deviation of all data) for Pp and Ppk. Leave USL or LSL blank for a one-sided specification.
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- Cp
- 1.00
- Cpk
- 0.67
- Cpu
- 0.67
- Cpl
- 1.33
Below 1.0: not capable
Expected out of spec (normal assumption): 22,782 PPM (two-sided total) (2.28 %) · above USL 22,750 · below LSL 31.67
PPM ↔ % ↔ sigma level
3.40 PPM = 0.0003400 % = 6.00 σ (short-term, with 1.5σ shift)
Convention: the sigma level adds a 1.5σ shift to the one-tailed z of the defect rate (Six Sigma / Motorola convention), so 3.4 PPM = 6σ and 66,807 PPM = 3σ. Untick the box for the plain z value (3.4 PPM = 4.5).
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Formulas
- Cp = (USL − LSL) / 6σ (two-sided specs only)
- Cpu = (USL − mean) / 3σ, Cpl = (mean − LSL) / 3σ, Cpk = min(Cpu, Cpl)
- Pp and Ppk use the same formulas with σ overall instead of σ within.
- Expected PPM = 10⁶ × [P(z > (USL − mean)/σ) + P(z > (mean − LSL)/σ)], assuming a normal distribution.
- Sigma level = z of the defect rate + 1.5 (1.5σ shift convention). Without the shift, 3.4 PPM is z = 4.5.
What Cpk value is good enough?
Many automotive customers ask for Cpk or Ppk of at least 1.67 for new processes and special characteristics, and 1.33 for ongoing production. Your customer's requirement (for example in the PPAP or supplier manual) decides. Check that the process is stable on a control chart first: a Cpk from an unstable process does not predict anything.
σ should come from at least 25 subgroups (≈100 values) or at least 30 individual values. With fewer, Cpk/Ppk has a wide confidence interval: treat it as preliminary. PPM estimates assume normality. Check with a normal probability plot, or use a non-normal method for skewed data.
Worked example (NIST/SEMATECH e-Handbook, section 6.1.6): USL 20, LSL 8, mean 16, σ 2 gives Cp = 1.00 and Cpk = 0.67. The defaults above load this example.
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