Verified calculation capability

Process Capability (Cp/Cpk) Calculation Capability

Design-stage Cp/Cpk from μ, σ, LSL, USL. Not in-control SPC and not Monte Carlo simulated indices. · Engineering · Process

Capability ID engineering.process.capability · version 1.0.0

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

Model

Cp: Cp = (USL − LSL) / (6σ)
Cpu: Cpu = (USL − μ) / (3σ)
Cpl: Cpl = (μ − LSL) / (3σ)
Cpk: Cpk = min(Cpu, Cpl)

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`lsl`	Lower specification limit	—	input / output
`usl`	Upper specification limit (must be > lsl)	—	input / output
`mu`	Process mean	—	input / output
`sigma`	Process standard deviation	—	input / output
`Cp`	—	—	output
`Cpk`	—	—	output
`Cpu`	—	—	output
`Cpl`	—	—	output

Assumptions / Validity

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

Assumptions

Design-stage from stated μ and σ — not in-control SPC
Not Monte Carlo simulated indices
Two-sided limits; USL > LSL
Normal-theory 6σ / 3σ formulas

Not supported

One-sided only (omit a limit)
subgroup SPC
gauge R&R ANOVA
Monte Carlo simulated capability. Pp/Ppk from observations is a different page.

Example

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

lsl=0 usl=12 mu=6 sigma=1 → Cp=2 Cpk=2

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Design-stage Cp, Cpk, Cpu, Cpl from stated μ and σ + O3 mpmath tabulated Cp/Cpk. Two-sided USL > LSL.. 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 · Design-stage Cp, Cpk, Cpu, Cpl from stated μ and σ + O3 mpmath tabulated Cp/Cpk. Two-sided USL > LSL.· View Manifest · CVP overview · Specification
Verified scope: Design-stage Cp, Cpk, Cpu, Cpl from stated μ and σ + O3 mpmath tabulated Cp/Cpk. Two-sided USL > LSL.
Assurance: Engineering
Declared partition coverage: PASS · 6/6 declared partitions (centered, off-center-high, off-center-low, negative-cpk, alias, invalid-domain)
Deferred: Not Pp/Ppk from a sample, not Cpm/Cpmk, not P/T = 1/Cp, not Monte Carlo simulated indices, not in-control SPC, and not a Cp≥1.33 verdict.
Calculation version: 1.0.0
Verification: 5/5 calculation tests · 1/1 legacy golden · 2/2 legacy boundary · 2/2 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 d45618000fe2
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: design-stage Cp/Cpk/Cpu/Cpl vs separate-module identities (≤2 ULP). Not Pp/Ppk, not Cpm, not P/T=1/Cp, not Monte Carlo, not an in-control SPC study. ≤2 ULP vs O3 applies only to the published tabulated Cp/Cpk vectors (centered, off-center, negative Cpk, aliases, σ=2, shifted limits, tight). It is not a whole-domain guarantee and does not cover Pp/Ppk, Cpm, P/T, or Monte Carlo simulated indices.
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 · 2/2 CVP boundary · 6/6 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: process-capability
Engine: process-capability
REST: POST /api/v1/calc/process-capability
MCP: execute_calculation with capability_id: "engineering.process.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

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.process.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.