Cp vs Cpk: process capability explained

Cp: could the process fit, if it were centered?

Cp = (USL − LSL) ÷ 6σ. It compares the width of the specification with the natural spread of the process, and ignores where the process is centered. A Cp of 1.0 means the process spread exactly fills the specification.

Cpk: does it fit where it actually sits?

Cpk = the smaller of (USL − mean) ÷ 3σ and (mean − LSL) ÷ 3σ. It measures the distance from the mean to the nearer specification limit, so it accounts for centering.

Cpk can never be larger than Cp. They are equal only when the process is perfectly centered, and the gap between them shows how much capability is being lost to off-centering rather than to variation. That tells you which problem to fix: shift the mean, or reduce the spread.

Cp and Cpk versus Pp and Ppk

Cp and Cpk use within-subgroup variation and describe what the process can do when it behaves, its short-term potential. Pp and Ppk use total, overall variation and describe what customers actually received over time. A large gap between Cpk and Ppk points to shifts and drifts between subgroups.

Before you trust the number

A capability index is only meaningful when its assumptions hold:

• The process is stable. Check a control chart first; capability of an unstable process predicts nothing.
• The measurement system is adequate, confirmed by measurement system analysis.
• The data are roughly normal, or a method suited to the distribution is used.
• The sample reflects normal operating variation, not one shift or one batch.