Cp, Cpk, Pp and Ppk explained

What process capability measures

Process capability compares how much a process varies with how much variation the specification allows. For a characteristic with a lower specification limit (LSL) and an upper specification limit (USL), the allowed spread is USL − LSL. A capable process fits comfortably inside it.

Cp and Cpk

Cp = (USL − LSL) / (6σ) describes the potential of the process: it ignores where the process is centred. Cpk = min((USL − μ) / 3σ, (μ − LSL) / 3σ) takes the mean μ into account and equals the distance to the nearest limit measured in units of 3σ. Cpk is never larger than Cp, and they are equal only when the process is perfectly centred. For one-sided specifications only the relevant side is used.

In Cp and Cpk, σ is a short-term, within-subgroup estimate. For individual measurements it is commonly estimated from the average moving range divided by 1.128.

A worked example

A diameter is specified as 10.00 ± 0.06 mm, so LSL = 9.94 and USL = 10.06. The process has a mean of 10.02 mm and a short-term standard deviation of 0.01 mm.

Cp = 0.12 / 0.06 = 2.00. Cpk = min((10.06 − 10.02) / 0.03, (10.02 − 9.94) / 0.03) = min(1.33, 2.67) = 1.33. The process has plenty of potential, but because it is running off-centre toward the upper limit, its capability is much lower.

Pp and Ppk

Pp and Ppk use the same formulas but with the overall standard deviation of all data, so they include drift and shifts between subgroups. They describe the performance actually delivered over the period rather than the short-term potential.

Why the gap matters

A Cpk that is high while Ppk is much lower means the process is capable in the short term but its mean is moving. Tool wear and thermal change are common causes. This is why drift detection and correlation with tooling matter as much as the index values themselves.

Qynetic computes these indices with deterministic, automatically tested code. They are not produced by a language model; AI is used to reason about the results.

Limits of the indices

The indices assume a stable process and, in their simplest form, roughly normal data. Check stability with a control chart before trusting a capability number, and use enough data: small samples give uncertain estimates.