{
  "capability_id": "engineering.uncertainty.pooled_sd",
  "tool_id": "pooled-sd",
  "engine": "pooled-sd",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-15T23:38:12.910Z",
  "engine_build": "2026-09-15",
  "test_count": 8,
  "passed": 8,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 0,
      "passed": 0
    },
    "boundary": {
      "total": 5,
      "passed": 5
    },
    "property": {
      "total": 3,
      "passed": 3
    }
  },
  "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/pooled-sd",
  "api": "https://www.calculatorx.com/api/v1/calc/pooled-sd",
  "schema_input": "https://www.calculatorx.com/schemas/engineering.uncertainty.pooled_sd.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/engineering.uncertainty.pooled_sd.output.json",
  "assumptions": [
    "Pooled standard deviation: s_p = √(Σ ν_i s_i² / Σ ν_i) from k≥2 stated groups. ν_i > 0 and finite.",
    "s_i ≥ 0. Both zero is valid (s_p = 0).",
    "Not Type A from one sample, not Welch–Satterthwaite ν_eff, and not ISO 21748 u of a mean."
  ],
  "limitations": [
    "Takes stated s_i and ν_i — not a single sample of observations",
    "k=1 is rejected so this cannot wrap Type A / identity s",
    "Does not compute Welch–Satterthwaite ν_eff",
    "Does not compute ISO 21748 u of a mean"
  ],
  "boundary_conditions": [
    "missing s or nu → MISSING_REQUIRED_INPUT",
    "k = 1 → VALUE_OUT_OF_RANGE",
    "length mismatch → INVALID_INPUT",
    "negative s_i → VALUE_OUT_OF_RANGE",
    "ν_i ≤ 0 → VALUE_MUST_BE_POSITIVE"
  ],
  "sources": [
    {
      "title": "JCGM 100:2008 — Evaluation of measurement data (GUM)",
      "section": "4.2.4 Type A evaluation from several series",
      "url": "https://www.bipm.org/en/publications/guides/gum.html",
      "supports": "Independent series of observations of the same measurand may be pooled: s_p² is the ν-weighted mean of the sample variances.",
      "kind": "standard"
    },
    {
      "title": "ISO 5725-2 — Repeatability and reproducibility of standard measurement methods",
      "section": "Pooled repeatability standard deviation",
      "supports": "s_p is the usual pooled-within estimate from several groups. This page takes stated s_i and ν_i rather than a collaborative-study table.",
      "kind": "standard"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:9ce4e6f368b473483310c22bdcf9392af1368150be6a13bececbd7f2dcfa96d7",
  "tests": [
    {
      "id": "boundary-pool",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "s": [
          1,
          7
        ],
        "nu": [
          1,
          1
        ]
      },
      "expect": {
        "s_p": 5,
        "nu": 2,
        "k": 2
      },
      "expectWarning": null,
      "actual": {
        "s_p": 5,
        "nu": 2,
        "k": 2,
        "s": [
          1,
          7
        ],
        "nu_i": [
          1,
          1
        ]
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-pool-equal",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "s": [
          5,
          5
        ],
        "nu": [
          3,
          8
        ]
      },
      "expect": {
        "s_p": 5
      },
      "expectWarning": null,
      "actual": {
        "s_p": 5,
        "nu": 11,
        "k": 2,
        "s": [
          5,
          5
        ],
        "nu_i": [
          3,
          8
        ]
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-pool-n",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "s": [
          1,
          7
        ],
        "n": [
          2,
          2
        ]
      },
      "expect": {
        "s_p": 5
      },
      "expectWarning": null,
      "actual": {
        "s_p": 5,
        "nu": 2,
        "k": 2,
        "s": [
          1,
          7
        ],
        "nu_i": [
          1,
          1
        ]
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-pool-one",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "s": [
          3
        ],
        "nu": [
          8
        ]
      },
      "expectError": "VALUE_OUT_OF_RANGE",
      "code": "VALUE_OUT_OF_RANGE",
      "error": "need at least two groups"
    },
    {
      "id": "boundary-pool-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "s": [
          1,
          7
        ]
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "nu is required"
    },
    {
      "id": "property-pool",
      "ok": true,
      "kind": "property",
      "detail": "5",
      "expect": 5,
      "actual": 5
    },
    {
      "id": "property-pool-equal",
      "ok": true,
      "kind": "property",
      "detail": "5",
      "expect": 5,
      "actual": 5
    },
    {
      "id": "property-pool-alias",
      "ok": true,
      "kind": "property",
      "detail": "5",
      "expect": 5,
      "actual": 5
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 8,
      "total": 8,
      "golden": 0,
      "boundary": 5,
      "property": 3
    },
    "contract_checks": {
      "passed": 4,
      "total": 4
    }
  },
  "evidence_core_generated_at": "2026-09-15T23:34:31.244Z",
  "rendered_at": "2026-09-15T23:38:12.910Z",
  "release_integrity": {
    "status": "verified",
    "scope": "workspace",
    "production_attestation_required": true,
    "calculation_version": "1.0.0",
    "artifacts": {
      "engine": "1.0.0",
      "page": "1.0.0",
      "capability": "1.0.0",
      "evidence": "1.0.0",
      "input_schema": "1.0.0",
      "output_schema": "1.0.0",
      "mcp_contract": "1.0.0"
    },
    "digests": {
      "input_schema_sha256": "9df2c14e2a0bd90df92a6b43f0ace6bbdf7a0291d6514b2febc035bdc4024748",
      "output_schema_sha256": "c655b77686e92e8138f442f7f6f36a4ead7cdd219d3a6d2b5f9f6e69859b2c5b",
      "evidence_sha256": "7a689be3009d3fbd03567ffbe37dfd4104aa0dd98b6e72d796c19c32c30f4705",
      "evidence_core_sha256": "7a689be3009d3fbd03567ffbe37dfd4104aa0dd98b6e72d796c19c32c30f4705",
      "capability_sha256": "327298b51321d12e66d776835ffe0c4d6ced3b64b664707c7e4c3dc408da5ef3",
      "engine_sha256": "9265836b6b06f498f3f985320eab21319806f5471a924aead2cf954a9b6ffd8f",
      "mcp_contract_sha256": "ef59a935293be4e8212bcd43a3fc15993093aab9a9136fa56d3a8d267774178c"
    },
    "contract_checks": {
      "total": 4,
      "passed": 4,
      "failed": 0,
      "items": [
        {
          "id": "release-artifacts-aligned",
          "status": "pass",
          "detail": "1.0.0"
        },
        {
          "id": "schema-valid-input-executes",
          "status": "pass"
        },
        {
          "id": "engine-success-output-validates-schema",
          "status": "pass"
        },
        {
          "id": "schema-rejects-incomplete-input",
          "status": "pass"
        }
      ]
    },
    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
  }
}