How to use it
- Choose measurements to paste raw data, or mean and σ if you already know them.
- For data, enter the values in the order they were produced; the order matters for the within σ.
- Enter the lower and upper specification limits (or only one of them).
- Read Cpk and Ppk, the separate upper and lower indices, the two σ estimates and the expected parts per million out of specification.
Formulas
- Cp = (USL − LSL) / 6σ.
- CPU = (USL − μ) / 3σ, CPL = (μ − LSL) / 3σ, Cpk = min(CPU, CPL).
- σ within = MR̄ / 1.128, where MR̄ is the mean absolute difference between consecutive measurements.
- σ overall = sample standard deviation, √(Σ(x − x̄)² / (n − 1)).
- Pp, PPU, PPL, Ppk: the same formulas with σ overall.
- ppm out of spec = 10⁶ × [P(Z > (USL − μ)/σ) + P(Z < (LSL − μ)/σ)].
Worked example
Twelve measurements 496, 498, 497, 499, 498, 500, 499, 501, 500, 502, 501, 503 against limits 494 and 506:
- mean 499.5; moving ranges add up to 17, MR̄ = 17 ÷ 11 = 1.5455, σ within = 1.5455 ÷ 1.128 = 1.3701;
- σ overall = 2.0671 (the data drift upwards);
- Cp = 12 ÷ (6 × 1.3701) = 1.46; CPL = 5.5 ÷ (3 × 1.3701) = Cpk 1.338;
- Ppk = 5.5 ÷ (3 × 2.0671) = 0.887; about 4,729.6 ppm out of spec with the overall σ.
A gap between Cpk and Ppk like this points to a process that shifts over time.
With mean and σ: μ = 500, σ = 1.5, limits 494 and 506 give Cp = Cpk = 12 ÷ 9 = 1.333 and 63.3 ppm.
Tips
- Check stability first. Capability indices only predict anything for a process in statistical control.
- Use enough data: a few dozen points give a rough estimate; σ from 10 values can be far off.
- Normality matters for the ppm figure; skewed processes need other methods.