{
  "capability_id": "engineering.process.cpmk",
  "tool_id": "cpmk",
  "engine": "cpmk",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-16T22:38:08.850Z",
  "engine_build": "2026-09-16",
  "test_count": 7,
  "passed": 7,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 0,
      "passed": 0
    },
    "boundary": {
      "total": 4,
      "passed": 4
    },
    "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/process-capability-cpmk",
  "api": "https://www.calculatorx.com/api/v1/calc/cpmk",
  "schema_input": "https://www.calculatorx.com/schemas/engineering.process.cpmk.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/engineering.process.cpmk.output.json",
  "assumptions": [
    "Taguchi Cpmk = min(USL−μ, μ−LSL)/(3√(σ²+(μ−target)²)) from stated μ, σ, LSL, USL, and target.",
    "Not Cpm (two-sided span), not Cpk (no target in the denominator), not Ppm, and not a 1.33 verdict."
  ],
  "limitations": [
    "Design-stage from stated μ and σ — not measured in-control SPC",
    "Not Cpm (that uses the two-sided span USL−LSL)",
    "Not Cpk (Cpk has no target in the denominator)",
    "Not Ppm (that uses sample s)",
    "This page does not issue a Cpmk≥1.33 verdict"
  ],
  "boundary_conditions": [
    "missing target → MISSING_REQUIRED_INPUT",
    "sigma ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "USL ≤ LSL → INVALID_INPUT"
  ],
  "sources": [
    {
      "title": "Pearn, Kotz, and Johnson — Distributional and inferential properties of process capability indices",
      "section": "Cpmk combines Cpk’s nearer side with Cpm’s Taguchi denominator",
      "supports": "Cpmk is not Cpm and not Cpk",
      "kind": "reference"
    },
    {
      "title": "ISO 22514-2 — Statistical methods in process management — Capability and performance",
      "section": "Capability vs performance; target-based indices",
      "supports": "This page is a design-stage target index, not overall sample Ppm",
      "kind": "standard"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:45301a6db44ca0b48d43808b1fd35723349c5f376c995afbcc4680636d07b1bc",
  "tests": [
    {
      "id": "boundary-cpmk",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "lsl": 0,
        "usl": 12,
        "mu": 6,
        "sigma": 1,
        "target": 6
      },
      "expect": {
        "Cpmk": 2,
        "offset": 0
      },
      "expectWarning": null,
      "actual": {
        "Cpmk": 2,
        "mu": 6,
        "sigma": 1,
        "target": 6,
        "offset": 0,
        "lsl": 0,
        "usl": 12
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-cpmk-shift",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "lsl": 0,
        "usl": 12,
        "mu": 7,
        "sigma": 1,
        "target": 6
      },
      "expect": {
        "Cpmk": 1.178511301977579
      },
      "expectWarning": null,
      "actual": {
        "Cpmk": 1.178511301977579,
        "mu": 7,
        "sigma": 1,
        "target": 6,
        "offset": 1,
        "lsl": 0,
        "usl": 12
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-cpmk-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "lsl": 0,
        "usl": 12,
        "mu": 6,
        "sigma": 1
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "target is required"
    },
    {
      "id": "boundary-cpmk-sigma",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "lsl": 0,
        "usl": 12,
        "mu": 6,
        "sigma": 0,
        "target": 6
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "sigma must be greater than zero"
    },
    {
      "id": "property-cpmk",
      "ok": true,
      "kind": "property",
      "detail": "2",
      "expect": 2,
      "actual": 2
    },
    {
      "id": "property-cpmk-shift",
      "ok": true,
      "kind": "property",
      "detail": "5/(3√2)",
      "expect": 1.178511301977579,
      "actual": 1.178511301977579
    },
    {
      "id": "property-cpmk-alias",
      "ok": true,
      "kind": "property",
      "detail": "2",
      "expect": 2,
      "actual": 2
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 7,
      "total": 7,
      "golden": 0,
      "boundary": 4,
      "property": 3
    },
    "contract_checks": {
      "passed": 4,
      "total": 4
    }
  },
  "evidence_core_generated_at": "2026-09-16T21:07:40.795Z",
  "rendered_at": "2026-09-16T22:38:08.850Z",
  "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",
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      "mcp_contract": "1.0.0"
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    "digests": {
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      "evidence_core_sha256": "ad2ed7e8955dbe0a14a1ee7f6acca2144709b68ab6705dad71e8b56ce7e85e1d",
      "capability_sha256": "d9d544f8670f04d7eb6a2f12e8025e8f2beb182bbb7d77e139438f05aaa13ba3",
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    },
    "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"
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      ]
    },
    "report": "https://www.calculatorx.com/.well-known/calculatorx-release-integrity.json"
  }
}