Verified calculation capability

Repeatability from duplicates Calculation Capability

ISO 5725 repeatability s_r = √(Σ d_i² / (2m)) from m≥2 duplicate differences. Not Type A from a sample of observations, not r = 2.8·s, and not AIAG GRR EV = R̄/d2. · Engineering · Measurement

Capability ID engineering.measurement.duplicate_sd · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Repeatability s

Repeatability s: s_r = √(Σ d_i² / (2m))

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`d`	Duplicate differences d_i = y1−y2. Aliases: diffs, differences, delta. Share-URL: comma-separated.	—	input / output
`y1`	First of each pair. Used with y2 when d is omitted.	—	input
`y2`	Second of each pair, same length as y1.	—	input
`s_r`	Repeatability standard deviation √(Σ d_i² / (2m))	—	output
`m`	Number of duplicate pairs	—	output

Assumptions / Validity

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

Assumptions

ISO 5725 duplicate-difference repeatability: s_r = √(Σ d_i² / (2m)) from m≥2 pairs. m=1 is rejected.
d_i may be negative or zero. Both zero is valid (s_r = 0).
Not Type A from a sample of observations, not r = 2.8·s, and not AIAG GRR EV = R̄/d2.

Not supported

Type A from a sample
r = 2.8·s
m=1 wrap of |d|/√2
AIAG GRR EV

Example

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

d=[6,8] → s_r=5

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: 8/8 calculation tests · golden 0/0 · boundary 5/5 · property 3/3
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: duplicate-sd
Engine: duplicate-sd
REST: POST /api/v1/calc/duplicate-sd
MCP: execute_calculation with capability_id: "engineering.measurement.duplicate_sd"
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 5725-2 — Repeatability and reproducibility of standard measurement methods — Repeatability variance from duplicate differences
ISO 5725-1 — Accuracy (trueness and precision) of measurement methods and results — Repeatability standard deviation s_r

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.measurement.duplicate_sd"}}}'

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