{
  "capability_id": "engineering.process.capability",
  "tool_id": "process-capability",
  "engine": "process-capability",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-16T22:03:43.732Z",
  "engine_build": "2026-09-16",
  "test_count": 5,
  "passed": 5,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 1,
      "passed": 1
    },
    "boundary": {
      "total": 2,
      "passed": 2
    },
    "property": {
      "total": 2,
      "passed": 2
    }
  },
  "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/process-capability",
  "api": "https://www.calculatorx.com/api/v1/calc/process-capability",
  "schema_input": "https://www.calculatorx.com/schemas/engineering.process.capability.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/engineering.process.capability.output.json",
  "assumptions": [
    "Design-stage from stated μ and σ — not in-control SPC",
    "Not Monte Carlo simulated indices",
    "Two-sided limits; USL > LSL",
    "Normal-theory 6σ / 3σ formulas"
  ],
  "limitations": [
    "Design-stage indices from μ and σ — not measured in-control SPC",
    "Not Monte Carlo simulated Cp/Cpk",
    "Two-sided LSL/USL required; USL must be greater than LSL"
  ],
  "boundary_conditions": [
    "sigma ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "USL ≤ LSL → INVALID_INPUT",
    "missing lsl/usl/mu/sigma → MISSING_REQUIRED_INPUT"
  ],
  "sources": [
    {
      "title": "NIST Engineering Statistics Handbook — Process Capability",
      "section": "6.1.6.1 Cp (process capability index)",
      "url": "https://www.itl.nist.gov/div898/handbook/pmc/section1/pmc16.htm",
      "supports": "Cp = (USL − LSL) / (6σ) from a stated process standard deviation",
      "kind": "reference"
    },
    {
      "title": "NIST Engineering Statistics Handbook — Process Capability",
      "section": "6.1.6.2 Cpk",
      "url": "https://www.itl.nist.gov/div898/handbook/pmc/section1/pmc162.htm",
      "supports": "Cpk = min(Cpu, Cpl) accounts for process centering; Cpu=(USL−μ)/(3σ), Cpl=(μ−LSL)/(3σ)",
      "kind": "reference"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:a1a60218799bb43689a9dedca524e31c07f128d905e389b519a0c93fbe7347c5",
  "tests": [
    {
      "id": "golden-cpk-center",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "lsl": 0,
        "usl": 12,
        "mu": 6,
        "sigma": 1
      },
      "expect": {
        "Cp": 2,
        "Cpk": 2
      },
      "expectWarning": null,
      "actual": {
        "Cp": 2,
        "Cpk": 2,
        "Cpu": 2,
        "Cpl": 2,
        "lsl": 0,
        "usl": 12,
        "mu": 6,
        "sigma": 1
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-cpk-sigma",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "lsl": 0,
        "usl": 12,
        "mu": 6,
        "sigma": 0
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "sigma must be greater than zero"
    },
    {
      "id": "boundary-cpk-limits",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "lsl": 12,
        "usl": 0,
        "mu": 6,
        "sigma": 1
      },
      "expectError": "INVALID_INPUT",
      "code": "INVALID_INPUT",
      "error": "usl must be greater than lsl"
    },
    {
      "id": "property-cpk-center",
      "ok": true,
      "kind": "property",
      "detail": "2",
      "expect": 2,
      "actual": 2
    },
    {
      "id": "property-cpk-shift",
      "ok": true,
      "kind": "property",
      "detail": "4/3",
      "expect": 1.3333333333333333,
      "actual": 1.3333333333333333
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 5,
      "total": 5,
      "golden": 1,
      "boundary": 2,
      "property": 2
    },
    "contract_checks": {
      "passed": 4,
      "total": 4
    }
  },
  "evidence_core_generated_at": "2026-09-16T04:33:21.940Z",
  "rendered_at": "2026-09-16T22:03:43.732Z",
  "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": "1fded02ee1287a641eb5645f574818b51c4a1e06e236456287f2b5303ffc5af9",
      "output_schema_sha256": "2c5af670b13dd55f0e6913e4c9a824fb041cece92dda81a6538a4698b5bf506b",
      "evidence_sha256": "6808ea0753d91b037943c5185c1c6df8aff9e2902086ac5e497792c462b35c99",
      "evidence_core_sha256": "6808ea0753d91b037943c5185c1c6df8aff9e2902086ac5e497792c462b35c99",
      "capability_sha256": "7670906d21ce2220968b0f709b804f380be961907c47eb3fa8f06395d1f7076a",
      "engine_sha256": "c8d4ccdbfeaf61d7b024d4e1babb0c2ba3b324c1b37bd0cb456a526d8d2b1bd1",
      "mcp_contract_sha256": "863098b311a7b17dc4b229a6302b90b3545b175f716e5d84772c7be8e9716b86"
    },
    "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"
  }
}