Process capability: Cp, Cpk, Pp and Ppk

01The indices

• Cp = (USL − LSL) / 6σ. Potential capability if the process were centred.
• Cpk = min(USL − μ, μ − LSL) / 3σ. Actual capability including centring.
• Pp and Ppk use the overall standard deviation of all data instead of the within-subgroup estimate, so they describe performance over the study period.

σ in Cp and Cpk is the short term or within-subgroup standard deviation, typically estimated from R̄/d₂ or s̄/c₄ of a control chart.

02Conditions for a valid study

The process must be in statistical control, shown with a control chart. Data should be approximately normal, or a suitable non-normal method used. The measurement system should be capable, see MSA. Sample size matters: indices from 30 parts have wide confidence intervals.

03Typical targets

Many buyers require Cpk ≥ 1.33 for ongoing production and ≥ 1.67 for initial studies or special characteristics. A Cpk of 1.33 corresponds to the nearest specification limit being four standard deviations from the mean.

04See it interactively

Move the mean and spread in the model below to see how Cp and Cpk change and how quickly expected nonconforming output rises when the process drifts.

05Common errors

• Calculating capability from unstable data.
• Using overall σ but calling the result Cpk.
• Ignoring non-normal distributions for characteristics such as flatness or runout.
• Reporting capability for characteristics with an incapable gauge.