CVP verified calculation capability

Process capability (Cpmk) Calculation Capability

Taguchi Cpmk = min(USL−μ, μ−LSL)/(3√(σ²+(μ−target)²)) from stated μ, σ, LSL, USL, and a target. Not Cpm, not Cpk, not Ppm, and not a Cpmk≥1.33 verdict.

Engineering · Process Capability ID engineering.process.cpmk version 1.0.1 CVP VERIFIED CURRENT Engineering

Model

Cpmk

Cpmk: Cpmk = min(USL − μ, μ − LSL) / (3 √(σ² + (μ − target)²))

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	—	input / output
`mu`	Process mean	—	input / output
`sigma`	Process standard deviation	—	input / output
`target`	Target value	—	input / output
`Cpmk`	Taguchi one-sided min	—	output
`offset`	μ − target	—	output

Assumptions / Validity

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

Assumptions

Taguchi Cpmk = min(USL−μ, μ−LSL)/(3√(σ²+(μ−target)²)) from stated μ, σ, LSL, USL, and target.
Not Cpm (two-sided span), not Cpk (no target in the denominator), not Ppm, and not a 1.33 verdict.

Not supported

Cpm
Cpk
Ppm
Cpmk≥1.33 verdict
P/T = 1/Cp

Example

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

lsl=0 usl=12 mu=6 sigma=1 target=6 → Cpmk=2

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Design-stage Taguchi Cpmk from stated μ, σ, LSL, USL, and a target, + O3 mpmath tabulated Cpmk.. 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 Taguchi Cpmk from stated μ, σ, LSL, USL, and a target, + O3 mpmath tabulated Cpmk.· View Manifest · CVP overview · Specification
Verified scope: Design-stage Taguchi Cpmk from stated μ, σ, LSL, USL, and a target, + O3 mpmath tabulated Cpmk.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (on-target, off-target, alias, awkward, invalid-domain)
Deferred: Not Cpm, not Cpk, not Ppmk from a sample, and not a Cpmk≥1.33 verdict.
Calculation version: 1.0.1
Verification: 7/7 calculation tests · 1/1 legacy golden · 3/3 legacy boundary · 3/3 legacy property
Production surface contract: 6/6
Versions: Calculation 1.0.1 · CVP protocol 1.0.0-proposed · Evidence 2026-09-24.o2-o3
Verification revision: 2026-09-24.o2-o3 · 1/1 property · digest 1bc90998298e
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: design-stage Taguchi Cpmk vs a separate-module identity (≤2 ULP). Not Cpm, not Cpk, and not a Cpmk≥1.33 verdict. ≤2 ULP vs O3 applies only to the published tabulated Cpmk vectors (on target, off target, below target, an alias, a wider σ, a target away from the midpoint, one awkward sample, and a tiny offset). It is not a whole-domain guarantee and does not cover Cpm, Cpk, or a Cpmk≥1.33 verdict.
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 · 3/3 CVP boundary · 6/6 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 3/3 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/cpmk' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"lsl":0,"usl":12,"mu":6,"sigma":1,"target":6},"calculation_version":"1.0.1"}'

{
  "inputs": {
    "lsl": 0,
    "usl": 12,
    "mu": 6,
    "sigma": 1,
    "target": 6
  },
  "calculation_version": "1.0.1"
}

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

Full REST contract: REST API docs.

Tool id: cpmk
Engine: cpmk
REST: POST /api/v1/calc/cpmk
MCP: execute_calculation with capability_id: "engineering.process.cpmk"
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

Pearn, Kotz, and Johnson — Distributional and inferential properties of process capability indices — Cpmk combines Cpk’s nearer side with Cpm’s Taguchi denominator
ISO 22514-2 — Statistical methods in process management — Capability and performance — Capability vs performance; target-based indices

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.process.cpmk"},"_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.process.cpmk","inputs":{"lsl":0,"usl":12,"mu":6,"sigma":1,"target":6},"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.