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: $Pp = \frac{USL - LSL}{6\sigma_{overall}}$ — uses overall (long-term) standard deviation.
• Ppk: $Ppk = minleft(\frac{USL - \bar{x}}{3\sigma_{overall}}, \frac{\bar{x} - LSL}{3\sigma_{overall}}\right)$ — 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.