Reduce variation.
Prove capability.

Process capability indices answer one question: "Can this process reliably produce output inside the customer's specification limits?" They compare the spread (and location) of your process data to the Voice of the Customer (USL/LSL). Cp and Cpk use SHORT-TERM (within-subgroup) variation — the inherent "process potential" you'd see if only common-cause noise existed, typically estimated from rational subgroups via the R-bar/d2 or S-bar/c4 method. Pp and Ppk use LONG-TERM (overall) variation — the ordinary sample standard deviation across all individual data points, which also captures shifts, drifts, and special causes over time. The "p" pair (Cp, Pp) ignores where the process mean sits relative to the spec — they only ask "if I centered this process perfectly, would the spread fit?" The "pk" pair (Cpk, Ppk) is centering-aware — it uses whichever spec limit the mean is closest to, so a well-spread-but-off-center process gets penalized. In practice: Cp/Cpk are computed early (capability study, often 20-25 subgroups, process demonstrated stable via control chart first); Pp/Ppk are computed over a longer historical window (e.g., a full production run) once you can't assume subgrouping removed all special causes. Comparing Cpk vs Ppk (the "capability gap") tells you how much of your long-term variation is shift/drift versus inherent noise — a big gap means the process is unstable over time even if each subgroup looks fine.

How to read it: Rule-of-thumb benchmarks (assuming normally distributed data — check normality before trusting these): • Index < 1.00: process NOT capable — will produce defects even if perfectly centered (for Cp/Pp) or is currently producing defects (Cpk/Ppk). • Index = 1.00: process spread exactly equals the spec width (±3σ = spec limits) — roughly 2,700 DPM at best, fragile, any drift causes defects. • Index = 1.33: common minimum acceptance threshold in industry (≈ 4σ performance, ~63 DPM at that side) — the traditional "capable" bar for an established process. • Index = 1.67: Six Sigma "entitlement" target for many programs (≈ 5σ). • Index ≥ 2.00: Six Sigma level (6σ) — ~3.4 DPM long-term with the standard 1.5σ shift assumption baked into the Cpk 1.5 ↔ Ppk figure. Always read Cpk/Ppk together with Cp/Pp: if Cp is comfortably ≥1.33 but Cpk is much lower, the SPREAD is fine but the process is OFF-CENTER — fix by shifting the mean (often cheap: adjustment, setpoint change) rather than reducing variation (usually expensive). If Cp itself is low, you have a fundamental variation-reduction problem (fixture, material, method) no amount of centering will fix. Compare Cpk to Ppk: Cpk ≈ Ppk means the process is stable over time (subgroup-to-subgroup variation ≈ overall variation); Cpk >> Ppk signals shifts/drifts/special causes are eating capability that a snapshot study didn't catch — investigate control-chart stability before trusting the Cpk number. Never quote Cp/Cpk without confirming the process is in statistical control (control chart) and data is reasonably normal (or use a transformed/non-normal method) — the formulas assume both.