Verified calculation capability

Gauge R&R Calculation Capability

AIAG Gauge R&R compose: GRR=√(EV²+AV²), TV=√(GRR²+PV²), %GRR, ndc. Optional range-method EV=R̄/d2. Not a full ANOVA study. · Engineering · Msa

Capability ID engineering.msa.gauge_rr · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON CVP Manifest Review policy

Model

Repeatability EV

Repeatability EV: EV = R̄ / d2
GRR: GRR = √(EV² + AV²)
TV: TV = √(GRR² + PV²)
%GRR: %GRR = 100 · GRR / TV
ndc: ndc = 1.41 · PV / GRR

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`ev`	Equipment variation (repeatability). Provide ev or rbar, not both.	—	input
`rbar`	Average range. EV = R̄/d2 when ev is omitted.	—	input / output
`d2`	d2 factor for range-method EV. Default 1.128 (n=2).	—	input / output
`av`	Appraiser variation (reproducibility)	—	input
`pv`	Part variation	—	input
`EV`	—	—	output
`AV`	—	—	output
`PV`	—	—	output
`GRR`	—	—	output
`TV`	—	—	output
`pct_grr`	—	—	output
`ndc`	—	—	output

Assumptions / Validity

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

Assumptions

AIAG compose: GRR=√(EV²+AV²), TV=√(GRR²+PV²), %GRR=100·GRR/TV, ndc=1.41·PV/GRR
Range-method EV = R̄/d2 (d2 defaults to 1.128 for n=2). Not a full ANOVA Gauge R&R.
Provide ev or rbar, not both

Not supported

full ANOVA Gauge R&R
nested study tables
%tolerance vs spec
X̄ and R control-chart constants beyond d2 for n=2

Example

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

ev=3 av=4 pv=12 → GRR=5 TV=13 pct_grr=500/13 ndc=3.384

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · AIAG Gauge R&R compose GRR/TV/%GRR/ndc from EV/AV/PV, optional range EV=R̄/d2 + O3 mpmath tabulated GRR.. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · AIAG Gauge R&R compose GRR/TV/%GRR/ndc from EV/AV/PV, optional range EV=R̄/d2 + O3 mpmath tabulated GRR.· View Manifest · CVP overview · Specification
Verified scope: AIAG Gauge R&R compose GRR/TV/%GRR/ndc from EV/AV/PV, optional range EV=R̄/d2 + O3 mpmath tabulated GRR.
Assurance: Engineering
Declared partition coverage: PASS · 6/6 declared partitions (stated-ev, range-ev, custom-d2, alias, pv-zero, invalid-domain)
Deferred: Not a full ANOVA Gauge R&R, not nested study tables, not %tolerance vs spec, not Cg/Cgk, and not X̄/R constants beyond d2 for n=2.
Calculation version: 1.0.0
Verification: 8/8 calculation tests · 1/1 legacy golden · 4/4 legacy boundary · 3/3 legacy property
Production surface contract: 4/4
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.o2-o3
Verification revision: 2026-09-16.o2-o3 · 3/3 property · digest 91696d47fa7d
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: AIAG GRR/TV/%GRR/ndc and range EV=R̄/d2 vs separate-module identities (≤2 ULP). Not full ANOVA, not %tolerance vs spec, not Cg. ≤2 ULP vs O3 applies only to the published tabulated GRR vectors (stated EV, range EV, custom d2, AV=0, PV=0, aliases, scale). It is not a whole-domain guarantee and does not cover full ANOVA or %tolerance vs spec.
Interfaces: PASS · UI (SSR) / REST / MCP
ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
CVP suite: 5/5 golden · 4/4 CVP boundary · 7/7 invalid · 3/3 property · 2/2 metamorphic · 8/8 O3 · 4/4 cross-interface · 4/4 CVP contract
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)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

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: gauge-rr
Engine: gauge-rr
REST: POST /api/v1/calc/gauge-rr
MCP: execute_calculation with capability_id: "engineering.msa.gauge_rr"
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

AIAG Measurement Systems Analysis (MSA) — Gauge R&R — %GRR and ndc
NIST Engineering Statistics Handbook — Repeatability — 2.4.5 Repeatability and reproducibility

Reference evidence classes: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior

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.msa.gauge_rr"}}}'

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