Verified calculation capability

Welch–Satterthwaite ν_eff Calculation Capability

Effective degrees of freedom ν_eff = u_c⁴ / Σ (u_i⁴ / ν_i) (GUM G.4). If uc is omitted, u_c is the uncorrelated RSS of u_i. Not combined RSS as a product page and not expanded U = k·u_c. · Engineering · Uncertainty

Capability ID engineering.uncertainty.welch_satterthwaite · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Effective degrees of freedom

Effective degrees of freedom: ν_eff = u_c⁴ / Σ (u_i⁴ / ν_i)
Combined (when uc omitted): u_c = √(Σ u_i²)

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`u`	Standard uncertainty components u_i. Share-URL: comma-separated.	—	input / output
`nu`	Degrees of freedom ν_i, same length as u. Use inf (JSON null) for Type B with infinite dof.	—	input / output
`uc`	Optional combined standard uncertainty. Default hypot(u).	—	input / output
`nu_eff`	Effective degrees of freedom. null when infinite.	—	output
`infinite`	—	—	output

Assumptions / Validity

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

Assumptions

JCGM 100:2008 G.4 Welch–Satterthwaite
If uc omitted, u_c = RSS of uncorrelated u_i
Infinite ν_i contribute 0 to the sum
Not GUM model combination and not expanded U = k·u_c

Not supported

GUM model combination
expanded U = k·u_c
t-table k lookup
correlated extra terms

Example

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

u=[1,1] nu=[8,8] → ν_eff=16

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: 10/10 calculation tests · golden 0/0 · boundary 6/6 · property 4/4
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: welch-satterthwaite
Engine: welch-satterthwaite
REST: POST /api/v1/calc/welch-satterthwaite
MCP: execute_calculation with capability_id: "engineering.uncertainty.welch_satterthwaite"
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

JCGM 100:2008 (GUM) — Evaluation of measurement data — G.4 Effective degrees of freedom: the Welch–Satterthwaite formula

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.uncertainty.welch_satterthwaite"}}}'

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