Cpk

Cpk (Process Capability Index, Centered) is the most commonly used capability index, measuring both process spread AND centering relative to the specification limits — $Cpk = minleft(\frac{USL - \bar{x}}{3\sigma}, \frac{\bar{x} - LSL}{3\sigma}\right)$, accounting for how close the process mean is to the nearest spec limit.

Cpk Interpretation

• Cpk = 1.0: Process mean is 3σ from the nearest spec limit — ~1,350 PPM on the near side.
• Cpk = 1.33: 4σ to nearest limit — ~32 PPM — standard minimum requirement.
• Cpk = 1.67: 5σ to nearest limit — ~0.3 PPM — automotive requirement.
• Cpk < 1.0: Process is producing out-of-spec product — immediate corrective action needed.

Why It Matters

• Practical: Cpk reflects actual process performance including centering — the realistic capability metric.
• Cpk vs. Cp: If Cpk < Cp, the process is off-center — centering adjustment can improve Cpk without reducing variation.
• Industry Standard: Cpk is the standard capability metric in semiconductor manufacturing — reported in qualification documents.

Cpk is the real-world capability — measuring how well the process actually performs relative to specifications, including both spread and centering.