Cp vs Cpk: Difference, Formulas, and Interpretation

Why is Cp acceptable but Cpk not — and which lever (centering or variation) do I pull first?

Cp = (USL − LSL) / (6σ) — the ratio of tolerance width to process spread. It assumes the process is centered.

Cpk = min[(USL − μ)/(3σ), (μ − LSL)/(3σ)] — the worst-case ratio of distance from the mean to the closer spec limit. Cpk ≤ Cp when both are calculated from the same data, specification limits, and sigma estimate.

When Cp = Cpk the process is centered. When Cpk < Cp the process has drifted toward one of the limits.

Reporting only Cp hides centering issues. A process with Cp = 1.67 and Cpk = 0.80 looks healthy on paper but is producing parts close to one limit. Customer scorecards, PPAP submissions, and SPC dashboards commonly request Cpk alongside the study method and stability evidence.

A material gap between Cp and Cpk is evidence of process centering loss. The required response depends on the Control Plan, characteristic classification, observed nonconformance, and customer requirements. Possible consequences include containment, corrective action, sorting, premium freight, and lost capacity.

Common automotive practice uses 1.33 for established production and 1.67 for some initial or launch studies, but the controlling value is always the applicable customer-specific requirement, drawing, Control Plan, or internal standard. Do not treat these values as universal pass/fail rules.

• Cp 1.67 / Cpk 1.67 — centered, capable.
• Cp 1.67 / Cpk 1.00 — strong potential, mean is drifting.
• Cp 0.90 / Cpk 0.85 — variation too high regardless of centering.

1. Verify the study is on a stable, single-stream, single-cavity dataset.
2. Confirm MSA (Gage R&R %TV) is acceptable for the tolerance.
3. Use within-subgroup σ (R̄/d₂ or s̄/c₄) for both Cp and Cpk.
4. Plot the histogram against USL/LSL to visualize offset vs spread.
5. Compute Cp = (USL − LSL) / 6σ and Cpk = min[(USL − μ), (μ − LSL)] / 3σ.
6. Compute k = |μ − target| / (tolerance/2); Cpk ≈ Cp × (1 − k).
7. If k dominates the loss, action = re-centering (offset, fixture, tool comp).
8. If Cp itself is low, action = variation reduction (DoE, source of variance study).
9. Re-run the study after the change with the same sampling design.
10. Update Control Plan and reaction plan with the new evidence.

• Mixing cavities, spindles, or lanes into one dataset — Cp collapses artificially.
• Using overall σ for Cp and within-subgroup σ for Cpk — mathematically incoherent.
• Calculating Cp on a one-sided characteristic (only USL or only LSL exists).
• Ignoring drift within the study window; the mean at hour 8 differs from hour 1.
• Reporting Cp/Cpk on an unstable process pulled from an out-of-control chart.

• Cp is the ceiling Cpk can ever reach for the current variation — no centering trick can exceed it.
• Reporting only Cp on a customer scorecard hides drift and is not defensible in PPAP.
• A Cp/Cpk gap that appears and disappears across shifts almost always indicates operator adjustment or setup drift, not machine capability.
• Cp is estimator-sensitive: switching from R̄/d₂ to pooled σ can change both indices without any process change.

• One-sided specifications — Cp is undefined; use Cpu or Cpl alone.
• Attribute (pass/fail) data — use defect-rate or Poisson-based methods.
• Non-normal data without transformation or a documented percentile method.
• Destructive tests where within-subgroup variation cannot be observed.

• Cpk vs Cp: Cpk ≤ Cp always; equality only when perfectly centered.
• Cpk vs Ppk: Cpk uses within-subgroup σ (short term); Ppk uses overall σ (long term). Cpk > Ppk normally.
• Cpk vs Cmk: Cmk is machine-only, single setup, short window — do not treat Cmk as production Cpk.
• Cpk vs Cpm: Cpm penalizes deviation from a target, not just from the nearest limit; useful when target-hit matters.

Move the mean and short-term variation to see why Cp can look acceptable while Cpk reveals lost centering margin.

1. Re-center the mean before chasing variation reduction.
2. Check fixture, tooling wear, and operator setup.
3. Verify measurement system (MSA) before drawing conclusions.
4. 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.

• Never compare Cp from one study with Cpk from another study — the σ estimators, sampling, and window may differ.
• A Cp/Cpk gap larger than 0.30 is an alarm, not a rounding artifact.
• If Cpk improves after re-centering but Cp does not, the process was never actually incapable — it was misaligned.

• off-target mean — A Cp/Cpk gap can require centering diagnosis.
• machining setup and offset context — Machining offsets make centering practical.

• ✓Control chart stable across the full study window
• ✓MSA acceptable for the tolerance (%TV or %tolerance rule per Control Plan)
• ✓Single-stream data (no mixed cavities, tools, or lots)
• ✓Same σ estimator used for Cp and Cpk
• ✓Two-sided specification confirmed (both USL and LSL exist)
• ✓Normality checked, or non-normal method documented
• ✓Cpk ≤ Cp verified numerically

• Process condition: statistical stability is required.
• Distribution assumption: use a distribution model justified for the data.
• Confirm process stability and measurement-system adequacy before interpreting a capability index.
• Use a justified distribution model or non-normal method when the normal model is unsuitable.