Within-subgroup sigma estimates the inherent process; overall sigma includes all sources including drift.

Capability Conversion

Cp vs Pp: Short-Term vs Long-Term

3 min read Last updated July 2026

Both Cp and Pp ignore centering. The difference is which sigma you use: within-subgroup for Cp, overall for Pp.

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The engineering question this page answers

Is my process variation entitled or realized — and is the gap between Cp and Pp telling me about instability?

Decision logic

Compute Cp using within-subgroup σ (σ_within = R̄/d₂ or S̄/c₄) ↓ Compute Pp using overall σ (sample standard deviation of all individuals) ↓ Ratio Pp / Cp close to 1 → process stable, sigma sources aligned ↓ Ratio Pp / Cp << 1 → between-subgroup variation is inflating overall σ ↓ Investigate the gap before publishing either number

Capability study readiness

Formula

Cp = (USL − LSL) / (6 × σ_within) Pp = (USL − LSL) / (6 × σ_overall) σ_within = R̄ / d₂ or S̄ / c₄ σ_overall = sample standard deviation of all data

Examples

Example. Turned diameter, USL−LSL = 0.20 mm. σ_within = 0.020 mm, σ_overall = 0.030 mm.

Cp = 0.20 / (6 × 0.020) = 1.67
Pp = 0.20 / (6 × 0.030) = 1.11
Ratio Pp / Cp = 0.66 → 34% of variation is between-subgroup drift, not inherent variation.
Engineering conclusion: capability entitlement is strong, but tool drift or setup variation is losing 0.56 index points. Fix the drift before capital investment.

Conversion conditions

Distribution modelA justified capability distribution model.

Specification modeltwo-sided

Tail conventioncontext-dependent

Centering assumptionBoth indices describe potential spread; neither includes mean offset.

Sigma basiscontext-dependent

Sigma-shift conventionnot-applicable

Output typeindex-comparison

Required inputs

LSL
USL
within-subgroup sigma for Cp
overall sigma for Pp
rational subgroup definition

Invertibility. Each index is calculated from the same specification width and its declared sigma basis.

Limitations

Mixed or unstable data makes the comparison diagnostic, not interchangeable.

Worked example and engineering limits

Worked example. With a 12-unit specification width, within sigma 1.0 gives Cp 2.00; overall sigma 1.2 gives Pp 1.67.

Failure case. Pooling unrelated streams or unstable periods makes a Cp-versus-Pp gap uninterpretable.

What cannot be inferred. Centering or customer acceptance.

Engineering next step. Review control charts and rational subgrouping before treating Pp as a long-term counterpart.

Common mistakes

Reporting Cp without stating that within-sigma was used.
Publishing only Cp when Pp is materially lower — hides instability.
Computing both with the same σ — makes the comparison meaningless.
Interpreting Cp > Pp as an error — it is a diagnostic, not a fault.

Engineering insight

Cp is a promise. Pp is a receipt. Investigate whenever they disagree — the process is telling you where to invest.

When NOT to use this metric

Rational subgrouping impossible (continuous processes, chemical batches) — Cp collapses to Pp.
Non-normal or heavy-tailed distributions.
Unstable processes — Cp is unreliable, Pp is only descriptive.

Relationship to other capability metrics

Cp vs Pp: Cp is the process entitlement, Pp is what the customer actually receives.
Gap Cp − Pp: Measures the cost of instability and between-subgroup variation.
Cp vs Cpk: Centering; Pp vs Ppk: Centering over the long run.

Recommended actions

Use the free Process Capability Calculator to compute Cp, Cpk, Pp, Ppk, sigma level, and predicted PPM from your measurement data — no sign-up required.

Continue the investigation

rational subgroup study design — A valid within-versus-overall comparison depends on study design.

Extend the same logic to centering with Cpk vs Ppk. If the gap is large, use Variation Too High or Improvement. Master formulas live in Process Capability Formula.

Verification checklist

Within-sigma computed from rational subgroups (R̄/d₂ or S̄/c₄)
Overall sigma computed from all individuals
Both indices reported with the same dataset
Gap explained before quoting either metric externally

Assumptions and applicability

Process condition: statistical stability is required.
Distribution assumption: approximately normal data.
PPM convention: nearest specification-limit tail.
Sigma-shift convention: no sigma shift applied.
Cpk alone identifies distance to the nearest specification limit; it does not determine total two-sided defects unless centering or both tail distances are known.
Predicted PPM is a model estimate, not a replacement for observed defect data.