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manufacturing-cpk-capability-calculator

Calculate and interpret process capability for manufacturing characteristics: Cp, Cpk, Pp, Ppk and Cpm with within-subgroup sigma (R-bar/d2, pooled S, MR-bar/1.128) and overall sigma, one-sided specifications, expected ppm within and overall vs observed ppm, a Bissell confidence interval for Cpk, Anderson-Darling normality test, and the percentile method for non-normal data. Explains off-centre processes, Ppk below Cpk from shifts and drift, wide intervals from small samples, and requirements such as PPAP Ppk 1.67, ongoing Cpk 1.33 and customer-specific thresholds; covers data prerequisites (MSA, stability, 100+ values) and non-normal causes and methods. Use when computing Cpk or Ppk for PPAP, a control plan, customer request or capability study, when Cpk and Ppk disagree, or when data look non-normal.

Manufacturing & Industrial Operations / Quality Management & ISO 9001v1.0.0Updated OCT 25 20262 references1 script

Capability answers whether a stable process fits its tolerance. The number is only meaningful if the gauge is capable, the process is in control, the data are representative and the distribution model fits. scripts/capability.py computes all the indices and also checks those conditions: normality, the gap between Cpk and Ppk, off-centring, observed vs expected defects and the confidence interval.

Trigger Conditions

Activate this skill when the user:

  • Needs Cpk / Ppk for a PPAP, control plan, customer or capability study
  • Has Cpk and Ppk that disagree, or a Cpk near the requirement
  • Has skewed or bounded data (flatness, runout, roughness) and asks how to compute capability
  • Asks what Cpk 1.33 means in ppm or how much data is needed

Control chart first: manufacturing-spc-chart-builder; gauge first: gage-rr-msa-analyzer.

Workflow

text
1. PREREQS -> gauge OK (Gage R&R), process stable (control chart), >= 100 representative values
2. RUN     -> python scripts/capability.py data.csv --value diameter --lsl 12.000 --usl 12.018 --subgroup hour
3. NORMAL? -> if Anderson-Darling p < 0.05: find why (mixture, drift, bound); --method percentile if natural
4. READ    -> Cp vs Cpk (centring), Cpk vs Ppk (stability), CI (enough data?), observed vs expected ppm
5. DECIDE  -> compare with the requirement (--target-index 1.33 / 1.67); plan centring or variation reduction

Output

text
Cp    1.38   Cpk   1.35   (95% CI 1.17 to 1.53)
Pp    1.17   Ppk   1.14
Expected ppm: within 36   overall 470   observed 8,000
  Ppk well below Cpk: between-subgroup variation (shifts, drift) - check the control chart.
  Observed 1 out-of-spec value(s) - far more than the normal model predicts: special causes or heavy tails.

Here Cpk passes 1.33 but the interval reaches 1.17, Ppk is 1.14 and a subgroup shifted: the process is not yet proven capable. Index definitions, ppm table, requirements and how to read patterns: capability-indices.md. Prerequisites, normality causes and non-normal methods: data-requirements-and-non-normal.md.

Output Format

Deliver:

  1. Data and conditions - n, subgrouping, gauge status, control-chart status, normality result.
  2. Indices - Cp, Cpk (with CI), Pp, Ppk, Cpm if a target is given; method used.
  3. Defect rates - expected within / overall and observed ppm.
  4. Interpretation - centring, stability, data sufficiency.
  5. Verdict vs the requirement and the improvement action (centre, stabilise, reduce variation).

Scripts

bash
python scripts/capability.py bore.csv --value diameter --lsl 12.000 --usl 12.018 --subgroup hour
python scripts/capability.py flatness.csv --value flatness --usl 0.05 --method percentile
python scripts/capability.py data.csv --value x --lsl 10 --usl 20 --target 15 --target-index 1.67 --json

Exit codes: 0 index meets --target-index (and data normal for the normal method), 1 below target or normality rejected, 2 usage or data error (fewer than 25 values, bad specs).

Additional Resources

FileContent
capability-indices.mdIndex formulas, ppm table, typical requirements, reading patterns, Cpk confidence interval
data-requirements-and-non-normal.mdPrerequisites, normality check causes, percentile / distribution / Box-Cox methods
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