CVP verified calculation capability

Process performance (Ppm) Calculation Capability

Overall Taguchi Ppm = (USL−LSL)/(6√(s²+(x̄−target)²)) from a sample. Not design-stage Cpm, not Pp/Ppk, and not a Ppm≥1.33 verdict.

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

Model

Ppm

Ppm: Ppm = (USL − LSL) / (6 √(s² + (x̄ − target)²))

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`values`	Process observations	—	input / output
`lsl`	Lower specification limit	—	input / output
`usl`	Upper specification limit	—	input / output
`target`	Target value	—	input / output
`ddof`	Delta degrees of freedom	—	input / output
`Ppm`	Overall Taguchi	—	output
`xbar`	—	—	output
`s`	—	—	output
`offset`	x̄ − target	—	output
`n`	—	—	output

Assumptions / Validity

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

Assumptions

Overall Taguchi Ppm = (USL−LSL)/(6√(s²+(x̄−target)²)) from a sample. s is summarizeSample.
Not design-stage Cpm, not Pp/Ppk (no target), and not a 1.33 verdict.

Not supported

design-stage Cpm
Pp/Ppk
Cpm≥1.33 / Ppm≥1.33 verdict
P/T = 1/Cp

Example

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

values=4,6,8 lsl=0 usl=12 target=6 → Ppm=1

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Overall Taguchi Ppm from a sample, LSL, USL, and a target, + O3 mpmath tabulated Ppm.. 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 · Overall Taguchi Ppm from a sample, LSL, USL, and a target, + O3 mpmath tabulated Ppm.· View Manifest · CVP overview · Specification
Verified scope: Overall Taguchi Ppm from a sample, LSL, USL, and a target, + O3 mpmath tabulated Ppm.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (on-target, off-target, alias, awkward, invalid-domain)
Deferred: Not design-stage Cpm, not Pp/Ppk, and not a Ppm≥1.33 verdict.
Calculation version: 1.0.1
Verification: 10/10 calculation tests · 1/1 legacy golden · 6/6 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 4ab6b02fc9cb
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: O2: overall Taguchi Ppm vs a separate-module sample identity (≤2 ULP). Not design-stage Cpm, not Pp/Ppk, and not a Ppm≥1.33 verdict. ≤2 ULP vs O3 applies only to the published tabulated Ppm vectors (on target, off target, below target, an alias, a wider sample, a target away from the midpoint, one awkward sample, and ddof=0). It is not a whole-domain guarantee and does not cover design-stage Cpm, Pp/Ppk, or a Ppm≥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 · 6/6 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/cpm-performance' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"values":[5,6,7],"lsl":0,"usl":12,"target":6},"calculation_version":"1.0.1"}'

{
  "inputs": {
    "values": [
      5,
      6,
      7
    ],
    "lsl": 0,
    "usl": 12,
    "target": 6
  },
  "calculation_version": "1.0.1"
}

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

Full REST contract: REST API docs.

Tool id: cpm-performance
Engine: cpm-performance
REST: POST /api/v1/calc/cpm-performance
MCP: execute_calculation with capability_id: "engineering.process.cpm_performance"
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

Chan, Cheng, and Spiring — A new measure of process capability: Cpm — Cpm = (USL−LSL)/(6√(σ²+(μ−T)²)); overall analog uses sample s
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.cpm_performance"},"_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.cpm_performance","inputs":{"values":[5,6,7],"lsl":0,"usl":12,"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.