Process Capability Calculator
Process capability indices — Cp, Cpk, Cpu and Cpl — from the specification limits and the process mean and standard deviation, with the share of output expected outside the limits.
Cp compares the width of the specification with the natural spread of the process (six standard deviations): 1.
How the process capability calculator works
Cp compares the width of the specification with the natural spread of the process (six standard deviations): 1.33 means the spec is a third wider than the process needs. Cpk also asks whether the process is centred: it is the distance from the mean to the nearer limit in units of three standard deviations. A centred process has Cpk = Cp; a Cpk of 1.33 corresponds to about 30 parts per million out of spec on that side.
Formula: Cp = (USL − LSL) ÷ 6σ; Cpu = (USL − μ) ÷ 3σ; Cpl = (μ − LSL) ÷ 3σ; Cpk = min(Cpu, Cpl)
Worked examples
| Inputs | Cpk | Note |
|---|---|---|
| Spec 9.5–10.5, mean 10.05, σ 0.12 | 1.25 | Cpk 1.25, Cp 1.39 |
| Centred with σ 0.1 | 1.667 | Cpk = Cp = 1.67 |
| Not capable: σ 0.2 | 0.833 | Cpk 0.83 — about 1.2% out of spec |
FAQFrequently asked questions
What Cpk do customers ask for?
Automotive and aerospace suppliers usually need Cpk ≥ 1.33 for ongoing production and 1.67 for new processes or safety-critical characteristics; 1.0 is the bare minimum, and below it the process is not capable.
What is the difference between Cp and Cpk?
Cp is potential capability if the process were perfectly centred; Cpk is actual, penalising an off-centre mean. A large gap between them says re-centre the process before trying to reduce its variation.
Cpk or Ppk?
Cpk uses the within-subgroup (short-term) standard deviation from a control chart; Ppk uses the overall long-term standard deviation of all the data. Ppk is usually lower and reflects what the customer sees over time.
Does the ppm assume a normal distribution?
Yes. Skewed or bounded characteristics (flatness, roughness) need a transformation or non-normal capability methods; the indices are still computed the same way by most software, but the ppm would be wrong.
Where these figures come from
- Nakajima (1988) — Introduction to TPM — the origin of Overall Equipment Effectiveness and its six big losses
- Safe Work Australia — the national work health and safety body
Last checked: September 2026. Definitions follow standard operations-management practice; where plants commonly differ, the page says so.