Verified calculation capability

Proficiency-testing z-score Calculation Capability

ISO 13528 z-score z = (ylab−xref)/σ_pt. σ_pt is the scheme standard deviation for proficiency assessment (SDPA), not laboratory u and not expanded U. |z| ≤ 2 pass, 2 < |z| < 3 warning, |z| ≥ 3 fail. Not zeta, not En, and not an ILAC G8 spec decision. · Engineering · Conformity

Capability ID engineering.conformity.z_score · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

z-score

z-score: z = (ylab − xref) / σ_pt
Decision: |z| ≤ 2 → pass; 2 < |z| < 3 → warning; |z| ≥ 3 → fail

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`ylab`	Laboratory / participant result. Aliases: y, x.	—	input / output
`xref`	Assigned or reference value. Aliases: X, ref.	—	input / output
`sigma`	Standard deviation for proficiency assessment σ_pt (SDPA). Aliases: sigma_pt, sdpa, s_pt. Not laboratory u and not expanded U.	—	input / output
`z`	—	—	output
`abs_z`	—	—	output
`decision`	—	—	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

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

Not supported

zeta (lab u)
En (expanded U)
TUR
ILAC G8 spec decision
computing σ_pt from a PT dataset

Example

One numerical check. The calculator page holds worked steps and FAQ.

ylab=2.5 xref=0 sigma=5 → z=0.5 pass

Open this example in the calculator

Trust

Review-policy: engine tested — automated tests, sources, version lock, and evidence published. Supplemental to CVP; not Domain Expert Review. See CVP and Review policy.

Tier: Engine tested — catalog token engine_tested
Calculation version: 1.0.0
Evidence tests: 13/13 calculation tests · golden 0/0 · boundary 7/7 · property 6/6
Engine tested: Yes
Source checked: Yes
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.0 (workspace artifacts agree)

Production attestation: Embedded snapshot: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-16T06:44:24.909Z
Semantic contract: PASS
Evidence attested at: 2026-09-16T06:44:24.203Z
Last production check: 2026-09-16T06:44:24.203Z
Public / cache: PASS
Origin: PASS

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 4/4.

Tool id: z-score
Engine: z-score
REST: POST /api/v1/calc/z-score
MCP: execute_calculation with capability_id: "engineering.conformity.z_score"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.0)
Versioned output schema: Immutable pin (1.0.0)

References

Human-readable sources plus CVP reference evidence classes.

Sources

ISO 13528 — Statistical methods for use in proficiency testing by interlaboratory comparison — z-score z = (x − X) / σ_pt
ISO/IEC 17043 — Conformity assessment — General requirements for the competence of proficiency testing providers — Performance statistics in proficiency testing

Try with an agent

Inspect this capability via same-origin MCP, then call execute_calculation.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"engineering.conformity.z_score"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.0.0) when reproducibility matters. Full protocol notes: MCP docs.