Is a 6σ process really 3.4 PPM?

Only under the explicitly labeled 1.5σ Six Sigma convention. With no shift, Z = 6 predicts about 0.001 PPM in the nearest tail, or about 0.002 PPM across two tails only when the process is centered.

Capability Conversion

Cpk to Sigma Level Conversion

3 min read Last updated July 2026

The sigma level of a process is the number of standard deviations between the mean and the closest spec. It is Cpk × 3 short-term.

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The engineering question this page answers

How do I express Cpk on the sigma scale my leadership understands without misrepresenting the process?

Decision logic

Confirm Cpk came from normal, stable, variables data ↓ Short-term sigma: Z_ST = 3 × Cpk ↓ Six Sigma long-term convention: Z_LT = 3 × Cpk + 1.5 ↓ Report both conventions if the audience is mixed

Formula

Z_ST = 3 × Cpk Z_LT = 3 × Cpk + 1.5 (Six Sigma convention)

Examples

Example. Injection-moulded seal groove width, Cpk = 1.33 (nearest tail, within-sigma, normality OK).

Z_ST = 3 × 1.33 = 4.0 sigma (short-term)
Z_LT = 4.0 + 1.5 = 5.5 sigma (Six Sigma reporting)
Same process: "4 sigma" on the shop-floor report, "5.5 sigma" on the executive dashboard. Both must be labelled.

Conversion conditions

Distribution modelNormal distribution, justified from stable study data.

Specification modelone-sided

Tail conventionnearest-tail

Centering assumptionThe result is distance to the nearest limit, not proof of centering.

Sigma basiswithin-subgroup

Sigma-shift conventionnone

Output typeindex-comparison

Required inputs

Cpk
declared sigma-shift convention

Invertibility. Nearest-specification sigma distance equals 3 × Cpk under the no-shift convention.

Limitations

Shifted long-term sigma cannot be derived without an explicit shift convention.
It does not infer observed defects.

Worked example and engineering limits

Worked example. Cpk 1.33 corresponds to 3.99 nearest-specification sigmas.

Failure case. Calling 3.99 sigma a shifted long-term Six Sigma level without a stated shift is incorrect.

What cannot be inferred. Process centering or total two-sided PPM.

Engineering next step. Use Cp, mean and both specification distances when centering is the decision.

Common mistakes

Publishing Z_LT without disclosing the 1.5σ shift.
Using overall σ to compute Cpk then reporting it as Z_ST — the sigma type must match the intent.
Comparing a Cpk-derived sigma against an attribute-yield sigma.
Rounding to the nearest half-sigma and losing engineering resolution near 1.33 / 1.67 thresholds.

Engineering insight

Sigma is an audience-facing translation of Cpk. Do not let the translation drive engineering decisions.

When NOT to use this metric

Non-normal or unstable processes — Z has no defensible meaning.
Multi-CTQ rollups — sigma level applies per characteristic.
Small samples where Cpk itself has ±0.3 confidence interval.

Relationship to other capability metrics

Cpk vs Z: Linear, factor of 3 — nothing more sophisticated.
Cpk vs Ppk sigma: Ppk × 3 is the "process-performance sigma" — a long-term view.
Cpk vs PPM: Z is the bridge; PPM is the tail.

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

See the inverse in Sigma → Cpk, and defect-rate translation in Cpk → PPM. For interpretation targets, see Cpk 1.33 and Cpk 1.67.

Verification checklist

Sigma convention (short/long) labelled
1.5σ shift disclosed if applied
σ type (within/overall) matches Cpk definition
Confidence interval on Cpk understood before reporting sigma to 1 decimal

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.