{
  "capability_id": "engineering.process.cpmk_performance",
  "tool_id": "cpmk-performance",
  "engine": "cpmk-performance",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-16T22:38:08.850Z",
  "engine_build": "2026-09-16",
  "test_count": 9,
  "passed": 9,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 0,
      "passed": 0
    },
    "boundary": {
      "total": 6,
      "passed": 6
    },
    "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-performance-ppmk",
  "api": "https://www.calculatorx.com/api/v1/calc/cpmk-performance",
  "schema_input": "https://www.calculatorx.com/schemas/engineering.process.cpmk_performance.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/engineering.process.cpmk_performance.output.json",
  "assumptions": [
    "Overall Taguchi Ppmk = min(USL−x̄, x̄−LSL)/(3√(s²+(x̄−target)²)) from a sample. s is summarizeSample.",
    "Not design-stage Cpmk, not Ppk (no target), not Ppm (two-sided span), and not a 1.33 verdict."
  ],
  "limitations": [
    "Overall sample s — not design-stage Cpmk from a stated σ",
    "Not Ppk (Ppk has no target in the denominator)",
    "Not Ppm (that uses the two-sided span USL−LSL)",
    "This page does not issue a Ppmk≥1.33 verdict"
  ],
  "boundary_conditions": [
    "missing target → MISSING_REQUIRED_INPUT",
    "n=1 with ddof=1 → VALUE_OUT_OF_RANGE",
    "s=0 and x̄=target → VALUE_MUST_BE_POSITIVE",
    "USL ≤ LSL → INVALID_INPUT"
  ],
  "sources": [
    {
      "title": "Pearn, Kotz, and Johnson — Distributional and inferential properties of process capability indices",
      "section": "Cpmk one-sided Taguchi; overall analog uses sample s",
      "supports": "Ppmk is the overall-sample counterpart of Cpmk",
      "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 overall performance, not design-stage Cpmk",
      "kind": "standard"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:cd2f6404e7c539f5af3c2d7fe063bd75dfc222cb63c8c8b53236902094d368a2",
  "tests": [
    {
      "id": "boundary-ppmk",
      "ok": true,
      "kind": "boundary",
      "inputs": {
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          6,
          8
        ],
        "lsl": 0,
        "usl": 12,
        "target": 6
      },
      "expect": {
        "Ppmk": 1,
        "xbar": 6,
        "s": 2,
        "offset": 0
      },
      "expectWarning": null,
      "actual": {
        "Ppmk": 1,
        "xbar": 6,
        "s": 2,
        "target": 6,
        "offset": 0,
        "n": 3,
        "ddof": 1,
        "lsl": 0,
        "usl": 12,
        "values": [
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          6,
          8
        ]
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-ppmk-shift",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "values": [
          7,
          8,
          9
        ],
        "lsl": 0,
        "usl": 12,
        "target": 6
      },
      "expect": {
        "Ppmk": 0.5962847939999439
      },
      "expectWarning": null,
      "actual": {
        "Ppmk": 0.5962847939999439,
        "xbar": 8,
        "s": 1,
        "target": 6,
        "offset": 2,
        "n": 3,
        "ddof": 1,
        "lsl": 0,
        "usl": 12,
        "values": [
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          9
        ]
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-ppmk-flat-off",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "values": [
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          8,
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        ],
        "lsl": 0,
        "usl": 12,
        "target": 6
      },
      "expect": {
        "Ppmk": 0.6666666666666666,
        "s": 0
      },
      "expectWarning": null,
      "actual": {
        "Ppmk": 0.6666666666666666,
        "xbar": 8,
        "s": 0,
        "target": 6,
        "offset": 2,
        "n": 3,
        "ddof": 1,
        "lsl": 0,
        "usl": 12,
        "values": [
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          8,
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        ]
      },
      "tol": 1e-12
    },
    {
      "id": "boundary-ppmk-n1",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "values": [
          1
        ],
        "lsl": 0,
        "usl": 12,
        "target": 6
      },
      "expectError": "VALUE_OUT_OF_RANGE",
      "code": "VALUE_OUT_OF_RANGE",
      "error": "sample variance needs at least two values"
    },
    {
      "id": "boundary-ppmk-flat-on",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "values": [
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          8,
          8
        ],
        "lsl": 0,
        "usl": 12,
        "target": 8
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "√(s²+(x̄−target)²) must be greater than zero"
    },
    {
      "id": "boundary-ppmk-missing",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "values": [
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          6,
          8
        ],
        "lsl": 0,
        "usl": 12
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "target is required"
    },
    {
      "id": "property-ppmk",
      "ok": true,
      "kind": "property",
      "detail": "1",
      "expect": 1,
      "actual": 1
    },
    {
      "id": "property-ppmk-shift",
      "ok": true,
      "kind": "property",
      "detail": "4/(3√5)",
      "expect": 0.5962847939999439,
      "actual": 0.5962847939999439
    },
    {
      "id": "property-ppmk-flat-off",
      "ok": true,
      "kind": "property",
      "detail": "2/3",
      "expect": 0.6666666666666666,
      "actual": 0.6666666666666666
    }
  ],
  "tier": "engine_tested",
  "verification": {
    "tests": {
      "passed": 9,
      "total": 9,
      "golden": 0,
      "boundary": 6,
      "property": 3
    },
    "contract_checks": {
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  },
  "evidence_core_generated_at": "2026-09-16T21:07:40.795Z",
  "rendered_at": "2026-09-16T22:38:08.850Z",
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    "scope": "workspace",
    "production_attestation_required": true,
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