pp and ppk

**Pp and Ppk** (Process Performance Indices) are **long-term capability metrics that use overall standard deviation (including between-subgroup variation)** — unlike Cp/Cpk which use within-subgroup σ, Pp/Ppk capture ALL sources of variation including lot-to-lot, shift-to-shift, and tool-to-tool differences. **Pp/Ppk vs. Cp/Cpk** - **Pp**: $Pp = frac{USL - LSL}{6sigma_{overall}}$ — uses overall (long-term) standard deviation. - **Ppk**: $Ppk = minleft(frac{USL - ar{x}}{3sigma_{overall}}, frac{ar{x} - LSL}{3sigma_{overall}} ight)$ — long-term, centered. - **Cp/Cpk**: Use within-subgroup σ — capture only short-term (inherent) variation. - **Ratio**: $Pp/Cp < 1$ indicates significant between-subgroup variation — process is less capable long-term. **Why It Matters** - **Reality Check**: Ppk shows what the customer actually experiences — including all variation sources. - **Gap**: The gap between Cpk and Ppk reveals controllable variation — reducing special causes closes this gap. - **Specification**: Some customers require both Cpk ≥ 1.67 AND Ppk ≥ 1.33 — both short and long-term capability. **Pp/Ppk** are **the long-term truth** — measuring actual process performance including ALL variation sources, not just inherent short-term capability.