Process Capability Index (Cpk)

What is this formula?

The Process Capability Index (Cpk) measures the actual capability of a process by considering both process variability and process centering.

Unlike Cp, Cpk accounts for the position of the process mean relative to the specification limits.

When to use it

Use this formula when:

- Evaluating real process performance.

- Measuring manufacturing capability.

- Identifying process drift.

- Supporting Six Sigma projects.

- Monitoring process improvements.

Example

A production process has:

USL = 50.5 mm

LSL = 49.5 mm

μ = 49.9 mm

σ = 0.10 mm

Formula:

Cpu = (USL − μ)/(3σ)

Cpl = (μ − LSL)/(3σ)

Substitution:

Cpu = (50.5 − 49.9)/(3×0.10)

Cpu = 2.00

Cpl = (49.9 − 49.5)/(3×0.10)

Cpl = 1.33

Result:

Cpk = min(2.00, 1.33)

Cpk = 1.33

Applications

- Statistical Process Control

- Six Sigma

- Manufacturing quality analysis

- Process optimization

- Industrial quality engineering

Note

Cpk is an empirical quality metric and assumes the process distribution is approximately normal and statistically stable. The lower of Cpu and Cpl determines the effective capability because it identifies the specification limit closest to the process mean.