CVP 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 1.0.1 CVP VERIFIED CURRENT Engineering

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	—	input / output
`xm`	Master / reference value	—	input / output
`T`	Characteristic tolerance span	—	input / output
`span`	Alias for T	—	input
`lsl`	Lower specification limit	—	input
`usl`	Upper specification limit	—	input
`tol`	Half-width; span = 2·tol	—	input
`frac`	Tolerance fraction used in Cg/Cgk	—	input / output
`ddof`	Delta degrees of freedom	—	input / output
`Cg`	—	—	output
`Cgk`	—	—	output
`s`	—	—	output
`xbar`	—	—	output
`bias`	—	—	output
`n`	—	—	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

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Cg = (frac T)/(6s) and Cgk = (frac T/2 − |x̄−xm|)/(3s), + O3 mpmath tabulated Cg.. 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 · Cg = (frac T)/(6s) and Cgk = (frac T/2 − |x̄−xm|)/(3s), + O3 mpmath tabulated Cg.· View Manifest · CVP overview · Specification
Verified scope: Cg = (frac T)/(6s) and Cgk = (frac T/2 − |x̄−xm|)/(3s), + O3 mpmath tabulated Cg.
Assurance: Engineering
Declared partition coverage: PASS · 7/7 declared partitions (alias, awkward, frac, limits, bias, centered, invalid-domain)
Deferred: Not Gauge R&R and not a capability verdict.
Calculation version: 1.0.1
Verification: 11/11 calculation tests · 1/1 legacy golden · 5/5 legacy boundary · 5/5 legacy property
Production surface contract: 6/6
Versions: Calculation 1.0.1 · CVP protocol 1.0.0-proposed · Evidence 2026-09-25.o2-o3
Verification revision: 2026-09-25.o2-o3 · 1/1 property · digest 48f057c8d64f
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: Cg and Cgk vs a separate-module sample identity (≤2 ULP). Not Gauge R&R. ≤2 ULP vs O3 applies only to the published tabulated Cg vectors. Not Gauge R&R.
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: 4/4 golden · 5/5 CVP boundary · 6/6 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 6/6 CVP contract
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.1 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.0.1 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 6/6.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/gauge-capability' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"values":[7,8,9],"xm":8,"T":30},"calculation_version":"1.0.1"}'

{
  "inputs": {
    "values": [
      7,
      8,
      9
    ],
    "xm": 8,
    "T": 30
  },
  "calculation_version": "1.0.1"
}

POST /api/v1/calc/gauge-capability. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

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 (1.0.1)
Versioned output schema: Immutable pin (1.0.1)

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

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

Try with an agent

Inspect, then execute. Same engine as REST and the human calculator.

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"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

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: execute_calculation' \
  -d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"engineering.msa.gauge_capability","inputs":{"values":[7,8,9],"xm":8,"T":30},"calculation_version":"1.0.1"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

Pin calculation_version (1.0.1) when the result must stay reproducible.

Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.