{
  "capability_id": "engineering.msa.gauge_capability",
  "tool_id": "gauge-capability",
  "engine": "gauge-capability",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-16T22:03:43.740Z",
  "engine_build": "2026-09-15",
  "test_count": 11,
  "passed": 11,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 0,
      "passed": 0
    },
    "boundary": {
      "total": 6,
      "passed": 6
    },
    "property": {
      "total": 5,
      "passed": 5
    }
  },
  "engine_tested": true,
  "expert_reviewed": false,
  "internally_reviewed": false,
  "review_kind": null,
  "source_checked": true,
  "reviewed_by": null,
  "reviewer_role": null,
  "last_reviewed": null,
  "expert_review": {
    "status": "optional_not_performed",
    "reviewer": null,
    "scope": [
      "formula",
      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance."
  },
  "internal_review": {
    "status": "not_applicable",
    "reviewer": null
  },
  "page": "https://www.calculatorx.com/calc/engineering/gauge-capability",
  "api": "https://www.calculatorx.com/api/v1/calc/gauge-capability",
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  "schema_output": "https://www.calculatorx.com/schemas/engineering.msa.gauge_capability.output.json",
  "assumptions": [
    "Type-1 Cg = (frac·T)/(6s), Cgk = (frac·T/2 − |x̄−xm|)/(3s). frac defaults to 0.2 (Bosch / VDA 5).",
    "s is overall sample s of repeats on a master. Not AIAG GRR, not Cp/Cpk, and not a Cg≥1.33 verdict.",
    "Exactly one spec form: lsl+usl, T/span, or half-width tol",
    "frac is a tolerance fraction (0 < frac ≤ 1), not coverage factor k"
  ],
  "limitations": [
    "Type-1 study on a master — not AIAG GRR compose (EV/AV/PV)",
    "Not process Cp/Cpk or Pp/Ppk",
    "Does not issue a Cg≥1.33 pass/fail",
    "frac is a tolerance fraction (default 0.2), not coverage factor k"
  ],
  "boundary_conditions": [
    "missing values, xm, or spec → MISSING_REQUIRED_INPUT",
    "n < 2 when ddof=1 → VALUE_OUT_OF_RANGE",
    "s = 0 → VALUE_MUST_BE_POSITIVE",
    "frac > 1 or more than one spec form → INVALID_INPUT"
  ],
  "sources": [
    {
      "title": "VDA Volume 5 — Capability of Measurement Processes",
      "section": "Type-1 study Cg, Cgk (20% of characteristic tolerance)",
      "supports": "Cg = 0.2·T / (6s); Cgk includes bias against the master",
      "kind": "standard"
    },
    {
      "title": "ISO 22514-7 — Capability of measurement processes",
      "section": "Cg and Cgk from a Type-1 study on a reference",
      "supports": "Gauge capability indices from repeats on a master versus a tolerance fraction",
      "kind": "standard"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:a7dfdfedfcf839816992c29c58b3dea40fd1fe7484554f97c9ab6690a526b421",
  "tests": [
    {
      "id": "boundary-cg",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "values": [
          7,
          8,
          9
        ],
        "xm": 8,
        "T": 30
      },
      "expect": {
        "Cg": 1,
        "Cgk": 1,
        "s": 1,
        "bias": 0
      },
      "expectWarning": null,
      "actual": {
        "Cg": 1,
        "Cgk": 1,
        "s": 1,
        "xbar": 8,
        "xm": 8,
        "bias": 0,
        "T": 30,
        "frac": 0.2,
        "n": 3,
        "ddof": 1,
        "values": [
          7,
          8,
          9
        ]
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-cg-bias",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "values": [
          6,
          7,
          8
        ],
        "xm": 8,
        "T": 30
      },
      "expect": {
        "Cg": 1,
        "Cgk": 0.6666666666666666
      },
      "expectWarning": null,
      "actual": {
        "Cg": 1,
        "Cgk": 0.6666666666666666,
        "s": 1,
        "xbar": 7,
        "xm": 8,
        "bias": 1,
        "T": 30,
        "frac": 0.2,
        "n": 3,
        "ddof": 1,
        "values": [
          6,
          7,
          8
        ]
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-cg-n1",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "values": [
          1
        ],
        "xm": 8,
        "T": 30
      },
      "expectError": "VALUE_OUT_OF_RANGE",
      "code": "VALUE_OUT_OF_RANGE",
      "error": "sample variance needs at least two values"
    },
    {
      "id": "boundary-cg-flat",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "values": [
          8,
          8,
          8
        ],
        "xm": 8,
        "T": 30
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "sigma must be greater than zero"
    },
    {
      "id": "boundary-cg-frac",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "values": [
          7,
          8,
          9
        ],
        "xm": 8,
        "T": 30,
        "frac": 2
      },
      "expectError": "INVALID_INPUT",
      "code": "INVALID_INPUT",
      "error": "frac must be ≤ 1 (tolerance fraction, default 0.2 — not coverage factor k)"
    },
    {
      "id": "boundary-cg-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "values": [
          7,
          8,
          9
        ],
        "T": 30
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "xm is required"
    },
    {
      "id": "property-cg",
      "ok": true,
      "kind": "property",
      "detail": "1",
      "expect": 1,
      "actual": 1
    },
    {
      "id": "property-cg-bias",
      "ok": true,
      "kind": "property",
      "detail": "2/3",
      "expect": 0.6666666666666666,
      "actual": 0.6666666666666666
    },
    {
      "id": "property-cg-limits",
      "ok": true,
      "kind": "property",
      "detail": "1",
      "expect": 1,
      "actual": 1
    },
    {
      "id": "property-cg-tol",
      "ok": true,
      "kind": "property",
      "detail": "1",
      "expect": 1,
      "actual": 1
    },
    {
      "id": "property-cg-frac",
      "ok": true,
      "kind": "property",
      "detail": "0.5",
      "expect": 0.5,
      "actual": 0.5
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 11,
      "total": 11,
      "golden": 0,
      "boundary": 6,
      "property": 5
    },
    "contract_checks": {
      "passed": 4,
      "total": 4
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  },
  "evidence_core_generated_at": "2026-09-15T10:14:13.310Z",
  "rendered_at": "2026-09-16T22:03:43.740Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
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    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
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