Verified calculation capability

MSA linearity Calculation Capability

OLS of measurement error ε = ylab − xref versus xref: slope = dε/d(xref). n≥3 paired points. Not a single-master bias, not Type-1 Cg, and not a %Linearity pass/fail. · Engineering · Msa

Capability ID engineering.msa.linearity · version 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

Model

Error

Error: εᵢ = ylabᵢ − xrefᵢ
Slope: b = Σ(xrefᵢ − x̄)(εᵢ − ē) / Σ(xrefᵢ − x̄)²
Intercept: a = ē − b·x̄

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`xref`	Reference values across the range. Aliases: X, ref, reference. Share-URL: comma-separated.	—	input / output
`ylab`	Indications paired with xref. Aliases: y, measured.	—	input / output
`slope`	—	—	output
`intercept`	—	—	output
`r_squared`	Coefficient of determination of ε vs xref. null when all errors are equal.	—	output
`n`	amount of substance	—	output
`xbar`	—	—	output
`ebar`	—	—	output
`error`	—	—	output

Assumptions / Validity

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

Assumptions

Ordinary least squares of ε = ylab − xref versus xref. slope = dε/d(xref).
n≥3 paired points. xref must not all be equal.
Not a single-master bias, not Type-1 Cg/Cgk, and not a %Linearity pass/fail.
Does not take T.

Not supported

%Linearity / process-variation verdict
Type-1 Cg/Cgk
single-master bias
pass/fail

Example

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

xref=[0,2,4] ylab=[0,3,6] → slope=0.5 intercept=0 r²=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: 9/9 calculation tests · golden 0/0 · boundary 6/6 · 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: linearity
Engine: linearity
REST: POST /api/v1/calc/linearity
MCP: execute_calculation with capability_id: "engineering.msa.linearity"
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) — Linearity and bias study — error versus reference
ISO 11095 — Linear calibration using reference materials — Ordinary least squares of response versus 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.linearity"}}}'

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