Verified calculation capability

Gauge capability (Cg/Cgk) Calculation Capability

Type-1 Cg/Cgk from repeats on a master: Cg=(frac·T)/(6s), Cgk=(frac·T/2−|x̄−xm|)/(3s). frac defaults to 0.2 (Bosch / VDA 5). Not AIAG GRR, not Cp/Cpk, and not a Cg≥1.33 verdict. · Engineering · Msa

Capability ID engineering.msa.gauge_capability · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Cg: Cg = (frac · T) / (6s)
Cgk: Cgk = (frac · T / 2 − |x̄ − xm|) / (3s)

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`values`	Repeats on a master. Sample s needs n≥2 when ddof=1. Share-URL: comma-separated. Alias: sample.	—	input / output
`xm`	Master / reference value. Aliases: xref, ref, x_m.	—	input / output
`T`	Characteristic tolerance span. Alias: span. Do not combine with lsl+usl or tol.	—	input / output
`span`	Alias for T.	—	input
`lsl`	Lower specification limit. Provide with usl, or use T or tol instead.	—	input
`usl`	Upper specification limit. Must be greater than lsl.	—	input
`tol`	Half-width; span = 2·tol. Do not combine with lsl+usl or T.	—	input
`frac`	Tolerance fraction used in Cg/Cgk. Default 0.2. Alias: k_tol. Not coverage factor k.	—	input / output
`ddof`	Delta degrees of freedom. 1 = Bessel (default), 0 = population.	—	input / output
`Cg`	—	—	output
`Cgk`	—	—	output
`s`	—	—	output
`xbar`	—	—	output
`bias`	—	—	output
`n`	amount of substance	—	output

Assumptions / Validity

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

Assumptions

Type-1 Cg = (frac·T)/(6s), Cgk = (frac·T/2 − |x̄−xm|)/(3s). frac defaults to 0.2 (Bosch / VDA 5).
s is overall sample s of repeats on a master. Not AIAG GRR, not Cp/Cpk, and not a Cg≥1.33 verdict.
Exactly one spec form: lsl+usl, T/span, or half-width tol
frac is a tolerance fraction (0 < frac ≤ 1), not coverage factor k

Not supported

AIAG GRR compose
process Cp/Cpk or Pp/Ppk
Cg≥1.33 verdict
coverage factor k as frac

Example

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

values=7,8,9 xm=8 T=30 → Cg=1 Cgk=1

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: 11/11 calculation tests · golden 0/0 · boundary 6/6 · property 5/5
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: gauge-capability
Engine: gauge-capability
REST: POST /api/v1/calc/gauge-capability
MCP: execute_calculation with capability_id: "engineering.msa.gauge_capability"
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

VDA Volume 5 — Capability of Measurement Processes — Type-1 study Cg, Cgk (20% of characteristic tolerance)
ISO 22514-7 — Capability of measurement processes — Cg and Cgk from a Type-1 study on a reference

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_capability"}}}'

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