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 1.0.0

Open calculator REST API MCP Evidence Evidence JSON Review policy

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. Sample s needs n≥2 when ddof=1. Share-URL: comma-separated. Alias: sample.	—	input / output
`lsl`	Lower specification limit	—	input / output
`usl`	Upper specification limit (must be > lsl)	—	input / output
`target`	Target value. Alias: x_target. Not tolerance span T.	—	input / output
`ddof`	Delta degrees of freedom. 1 = Bessel (default), 0 = population.	—	input / output
`Ppm`	Overall Taguchi (USL−LSL)/(6√(s²+(x̄−target)²))	—	output
`xbar`	—	—	output
`s`	—	—	output
`offset`	x̄ − target (signed)	—	output
`n`	amount of substance	—	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

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: 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 (1.0.0)
Versioned output schema: Immutable pin (1.0.0)

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

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.cpm_performance"}}}'

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