cpk

**Cpk** (Process Capability Index, Centered) is the **most commonly used capability index, measuring both process spread AND centering relative to the specification limits** — $Cpk = minleft(frac{USL - ar{x}}{3sigma}, frac{ar{x} - LSL}{3sigma} ight)$, 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.