Process capability: Cp, Cpk, Pp, and Ppk

Learning objectives

• Explain Cp, Cpk, Pp and Ppk in plain language.
• Calculate short- and long-term capability from a small sample.
• Interpret a capability result against a garment tolerance.

Two flavours of capability

Cp and Cpk use the within-subgroup standard deviation. They describe how the process could perform if the only variation present were short-term. Pp and Ppk use the overall standard deviation and describe how it actually performed across the whole study.

Cpk and Ppk are the indices that also count how well the process is centred inside the tolerance. A high Cp with a low Cpk means precision without accuracy.

Formulas in words

• Cp = (Upper spec − Lower spec) ÷ (6 × short-term standard deviation).
• Cpk = min[(Upper spec − mean), (mean − Lower spec)] ÷ (3 × short-term standard deviation).
• Pp and Ppk use the same formulas but with the overall standard deviation.

Garment-factory example

A polo chest-width tolerance is 52 ± 1 cm. A shift measures 30 shirts and finds mean 52.3 cm and overall standard deviation 0.35 cm. Ppk = min(52.7, 51.3 side) ÷ (3 × 0.35) = min(0.4, 1.0) ÷ 1.05 ≈ 0.38. The chest is centred high; the upper edge, not the process spread, is the risk.

Method

1. Measure at least 25–30 consecutive pieces or five subgroups of five.
2. Check the data are stable on a control chart before trusting capability.
3. Report both Cpk and Ppk; the gap is a fingerprint of assignable variation.
4. Never quote capability without stating the tolerance and sample size.

Common mistakes

• Reporting a single Cpk value from unstable data.
• Confusing Cp (spread only) with Cpk (spread and centring).