{
  "capability_id": "engineering.conformity.z_score",
  "tool_id": "z-score",
  "engine": "z-score",
  "calculation_version": "1.0.0",
  "generated_at": "2026-09-16T22:38:08.853Z",
  "engine_build": "2026-09-16",
  "test_count": 13,
  "passed": 13,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 0,
      "passed": 0
    },
    "boundary": {
      "total": 7,
      "passed": 7
    },
    "property": {
      "total": 6,
      "passed": 6
    }
  },
  "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
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  "page": "https://www.calculatorx.com/calc/engineering/proficiency-z-score",
  "api": "https://www.calculatorx.com/api/v1/calc/z-score",
  "schema_input": "https://www.calculatorx.com/schemas/engineering.conformity.z_score.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/engineering.conformity.z_score.output.json",
  "assumptions": [
    "ISO 13528 z-score with scheme SDPA σ_pt",
    "|z| ≤ 2 is pass; 2 < |z| < 3 is warning; |z| ≥ 3 is fail",
    "Not zeta (lab u), not En (expanded U), not TUR, and not an ILAC G8 spec decision"
  ],
  "limitations": [
    "σ_pt is the scheme SDPA — this page does not compute lab u or U = k·u",
    "Not the zeta-score (that uses √(ulab²+uref²))",
    "Not the normalized error En (that uses already-expanded U)",
    "Not TUR and not an ILAC G8 specification decision on y",
    "|z| ≤ 2 is pass; 2 < |z| < 3 is warning; |z| ≥ 3 is fail"
  ],
  "boundary_conditions": [
    "missing ylab, xref, or sigma → MISSING_REQUIRED_INPUT",
    "sigma ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "ulab / Ulab are not aliases for σ_pt"
  ],
  "sources": [
    {
      "title": "ISO 13528 — Statistical methods for use in proficiency testing by interlaboratory comparison",
      "section": "z-score z = (x − X) / σ_pt",
      "supports": "z uses the standard deviation for proficiency assessment, not laboratory u; |z| ≤ 2 / 2–3 / ≥ 3 interpretation",
      "kind": "standard"
    },
    {
      "title": "ISO/IEC 17043 — Conformity assessment — General requirements for the competence of proficiency testing providers",
      "section": "Performance statistics in proficiency testing",
      "supports": "z-score is a PT performance statistic distinct from En and zeta",
      "kind": "standard"
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  "methods": [],
  "fingerprint": "sha256:005a98a05f53b8cdb1bff1075587cee01ef5f939a82532b366567b123540b02b",
  "tests": [
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      "ok": true,
      "kind": "boundary",
      "inputs": {
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        "xref": 0,
        "sigma": 5
      },
      "expect": {
        "z": 0.5,
        "abs_z": 0.5,
        "decision": "pass"
      },
      "expectWarning": null,
      "actual": {
        "z": 0.5,
        "abs_z": 0.5,
        "decision": "pass",
        "ylab": 2.5,
        "xref": 0,
        "sigma": 5
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      "tol": 1e-12
    },
    {
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      "ok": true,
      "kind": "boundary",
      "inputs": {
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        "xref": 0,
        "sigma": 5
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      "expect": {
        "z": 2,
        "decision": "pass"
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      "expectWarning": null,
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        "abs_z": 2,
        "decision": "pass",
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        "sigma": 5
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      "tol": 1e-12
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        "sigma": 5
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        "decision": "warning"
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        "abs_z": 2.5,
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        "sigma": 5
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      "tol": 1e-12
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      "kind": "boundary",
      "inputs": {
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        "xref": 0,
        "sigma": 5
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      "expect": {
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        "decision": "fail"
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        "abs_z": 3,
        "decision": "fail",
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        "xref": 0,
        "sigma": 5
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      "tol": 1e-12
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    {
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      "ok": true,
      "kind": "boundary",
      "inputs": {
        "xref": 0,
        "sigma": 5
      },
      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "ylab is required"
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      "id": "boundary-z-sigma",
      "ok": true,
      "kind": "boundary",
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        "xref": 0,
        "sigma": 0
      },
      "expectError": "VALUE_MUST_BE_POSITIVE",
      "code": "VALUE_MUST_BE_POSITIVE",
      "error": "sigma must be greater than zero"
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      "id": "boundary-z-ulab",
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      "kind": "boundary",
      "inputs": {
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        "xref": 0,
        "ulab": 5
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      "expectError": "MISSING_REQUIRED_INPUT",
      "code": "MISSING_REQUIRED_INPUT",
      "error": "sigma is required"
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      "actual": 0.5
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      "actual": 2
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      "actual": 0.5
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      "expect": 0.5,
      "actual": 0.5
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  "tier": "engine_tested",
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      "total": 13,
      "golden": 0,
      "boundary": 7,
      "property": 6
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