{
  "capability_id": "engineering.conformity.z_prime",
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  "engine": "z-prime",
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  "passed": 12,
  "failed": 0,
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      "total": 6
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    "property": {
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  "expert_reviewed": false,
  "internally_reviewed": false,
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  "reviewer_role": null,
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      "sources",
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    ],
    "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance."
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  "internal_review": {
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    "reviewer": null
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  "api": "https://www.calculatorx.com/api/v1/calc/z-prime",
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  "schema_output": "https://www.calculatorx.com/schemas/engineering.conformity.z_prime.output.json",
  "assumptions": [
    "ISO 13528 z′ = (ylab−xref)/√(σ_pt²+u(x_pt)²)",
    "σ_pt > 0 and u(x_pt) > 0 — u(x_pt)=0 is not a z-score wrap",
    "Not z-score, not zeta, and not En"
  ],
  "limitations": [
    "Requires σ_pt > 0 and u(x_pt) > 0 — this page does not wrap z-score",
    "Not the z-score (that divides by σ_pt alone)",
    "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"
  ],
  "boundary_conditions": [
    "missing ylab, xref, sigma, or u_xref → MISSING_REQUIRED_INPUT",
    "σ_pt ≤ 0 or u(x_pt) ≤ 0 → VALUE_MUST_BE_POSITIVE",
    "ulab is not an alias for u_xref"
  ],
  "sources": [
    {
      "title": "ISO 13528 — Statistical methods for use in proficiency testing by interlaboratory comparison",
      "section": "z′ score when the uncertainty of the assigned value is not negligible",
      "supports": "z′ = (x − x_pt) / √(σ_pt² + u²(x_pt)). |z′| bands match the z-score bands.",
      "kind": "standard"
    },
    {
      "title": "ISO/IEC 17043 — Conformity assessment — General requirements for the competence of proficiency testing providers",
      "section": "Performance evaluation using z′",
      "supports": "z′ is a proficiency-testing statistic that keeps the assigned-value uncertainty in the denominator. It is not a z-score and not En.",
      "kind": "standard"
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      "golden": 1,
      "boundary": 6,
      "property": 5
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  "evidence_core_generated_at": "2026-09-24T21:41:40.192Z",
  "rendered_at": "2026-10-22T08:54:34.783Z",
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