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.

What sigma level is Cpk 1.33?

Cpk 1.33 corresponds to a short-term sigma level of approximately 4.0 because 1.33 × 3 = 3.99.

Should I add 1.5 sigma to Cpk × 3?

No, not by default. Cpk × 3 is the short-term distance to the nearest specification limit. Add 1.5 only when your organization explicitly uses the long-term Six Sigma reporting convention.

Capability Conversion

Cpk to Sigma Level Calculator and Conversion Table

3 min read Last updated July 2026

Convert Cpk to a short-term sigma level by multiplying Cpk by 3. Use the 1.5 sigma shift only when your Six Sigma reporting convention explicitly requires it.

Open the Process Capability Calculator Quality Statistics Knowledge Center

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.