When the process has no between-subgroup variation — i.e. it is perfectly stable over time.

Capability Conversion

Cpk vs Ppk: Differences and Reporting

3 min read Last updated July 2026

Cpk is the short-term, in-control capability. Ppk is the long-term, real-world capability including drift.

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The engineering question this page answers

Is my process short-term capable but long-term drifting — and how do I quantify the drift the customer sees?

Decision logic

Compute Cpk with within-sigma; Ppk with overall sigma; both on the same dataset ↓ Ratio Ppk / Cpk close to 1 → process stable and long-term = short-term ↓ Ratio Ppk / Cpk << 1 → drift, tool wear, or between-shift variation ↓ For PPAP submissions: Ppk during initial run, Cpk once stable and demonstrated

Capability study readiness

Formula

Cpk = min( (USL − x̄) / (3 σ_within), (x̄ − LSL) / (3 σ_within) ) Ppk = min( (USL − x̄) / (3 σ_overall), (x̄ − LSL) / (3 σ_overall) )

Examples

Example. Stamped hole diameter over a 30-day production window. x̄ = 6.02, USL = 6.10, LSL = 5.90, σ_within = 0.020, σ_overall = 0.028.

Cpk = min( (6.10 − 6.02)/(3×0.020), (6.02 − 5.90)/(3×0.020) ) = min(1.33, 2.00) = 1.33
Ppk = min( 0.08/(3×0.028), 0.12/(3×0.028) ) = min(0.95, 1.43) = 0.95
Ratio Ppk / Cpk = 0.71 → material long-term drift toward USL.
Engineering conclusion: short-term acceptable, long-term reject. Investigate tool-wear compensation cycle before requalifying.

Conversion conditions

Distribution modelA justified capability distribution model.

Specification modeltwo-sided

Tail conventionnearest-tail

Centering assumptionBoth indices use the nearest specification limit and the same mean.

Sigma basiscontext-dependent

Sigma-shift conventionnot-applicable

Output typeindex-comparison

Required inputs

mean
LSL
USL
within sigma for Cpk
overall sigma for Ppk
same study window and population

Invertibility. Both are calculated from the same limits and mean using their declared sigma basis.

Limitations

Different windows or populations cannot be interpreted as a pure short-term versus long-term difference.

Worked example and engineering limits

Worked example. With mean 10, limits 4 and 16, within sigma 1.0 gives Cpk 2.00; overall sigma 1.2 gives Ppk 1.67.

Failure case. Comparing Cpk from a setup study with Ppk from another production period is not diagnostic.

What cannot be inferred. A single root cause; a lower Ppk may indicate drift or between-subgroup variation.

Engineering next step. Stratify by time, tool, cavity or lot to locate the additional long-term variation.

Common mistakes

Reporting Cpk from a 25-piece PPAP as if it were long-term performance.
Comparing customer-observed defect rate against Cpk instead of Ppk.
Using overall σ in the Cpk formula (or within σ in the Ppk formula) — invalidates both.
Ignoring the Cpk − Ppk gap when writing corrective actions.

Engineering insight

A Cpk that hides a poor Ppk is a warranty problem waiting to happen. Track both, publish both, act on the smaller.

When NOT to use this metric

Non-normal data — index inflation on either side.
Single-batch production — no long-term data exists yet, Ppk is only descriptive.
Autocorrelated data — σ_within is compressed, Cpk is optimistic.

Relationship to other capability metrics

Cpk vs Ppk: Short vs long-term view of the same design intent.
Gap Cpk − Ppk: Direct measure of process drift or between-subgroup variation.
Ppk vs observed PPM: Ppk is the correct predictor of what the customer will see.

Interactive capability metrics explorer

Compare short-term and overall variation to see why Cpk and Ppk can diverge across a production study.

Illustration only · LSL 0 / USL 100 / Target 50

Interactive learning model — use Qhubio’s Process Capability Calculator with actual time-ordered measurements and approved specification limits for a real engineering study.

Explore the inputs

Process mean50

Move the process centre toward either specification limit.

Short-term variation (σwithin)10

Represents short-term, within-process variation.

Overall variation (σoverall)10

Represents long-term variation across the study period.

Preset scenarios

Scenario names describe illustrative inputs only. “Stable” does not establish statistical stability; “drift” does not establish a cause.

Short-term variationOverall variation

Illustrative normal curves · shaded zones are outside specifications. Coincident curves overlap when the two variation inputs are equal.

CpPotential capability: 1.67; More margin; Specification width compared with short-term variation.
CpkActual short-term capability: 1.67; More margin; Short-term variation adjusted for process centering.
PpOverall performance: 1.67; More margin; Specification width compared with overall variation.
PpkActual long-term performance: 1.67; More margin; Overall variation adjusted for process centering.

Your applicable customer, drawing, Control Plan or internal requirement governs acceptance.

What this model illustrates

Cp and Cpk are close in this model. The process is approximately centred within the specification.

Short-term and overall variation are the same in this illustrative input, so Cp/Pp and Cpk/Ppk are close.

Model limitations. Normal curves are illustrative, not a normality test. This model does not establish stability, measurement-system or Gage R&R adequacy, or customer acceptance. Overall variation is not forced above short-term variation: real-study sigma estimates depend on sampling, rational subgrouping, study design and estimator.

Cp = (USL − LSL) / (6σwithin); Cpk = min[(USL − M) / (3σwithin), (M − LSL) / (3σwithin)]. Pp and Ppk use the same formulas with σoverall. Calculations retain full precision; displayed indices are rounded to two decimals.

Ready to analyse real measurements?

Use Qhubio’s free Process Capability & Performance Calculator with time-ordered data and actual specification limits.

Open Process Capability Calculator Learn how to run a defensible capability study

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

drift or between-subgroup variation — A Cpk/Ppk gap can expose centering or time effects.
PPAP and long-term reporting context — Automotive reporting requires context for long-term performance.

Pair with Cp vs Pp, drill into centering with Not Centered, and address drift via Improvement. For target thresholds see Cpk 1.33.

Verification checklist

Same dataset for both indices
Sigma sources correctly assigned (within → C, overall → P)
Long-term window covers real production variation (shift, day, tool, lot)
Gap explicitly addressed in the capability report

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.