# measurement-uncertainty-mcp

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**A Model Context Protocol server for GUM measurement uncertainty analysis. Built for ISO/IEC 17025 calibration labs, ISO 10012:2026 measurement management systems, and KOLAS / A2LA / UKAS accredited testing.** No equivalent MCP server was found in a prior-art search (2026-07); that is not the same as being the first, and no claim of primacy is made here.

Compute Type A/B uncertainties, combined standard uncertainty u_c, effective degrees of freedom ν_eff via Welch-Satterthwaite, expanded uncertainty U with coverage factor k, Monte Carlo propagation per JCGM 101:2008, and apply pre-built KOLAS-ready uncertainty budgets — directly from Claude Desktop, Cursor, Windsurf, or any MCP client. No spreadsheet. No vendor lock-in. Standards-referenceable to JCGM 100:2008.

Now live on MCPize: **https://measurement-uncertainty.mcpize.run**

## Why now — ISO 10012:2026

ISO 10012:2026 was published in February 2026 — the first revision since 2003. The standard introduces a stronger, risk-based approach and adds practical guidance on **measurement uncertainty, Test Uncertainty Ratio (TUR), and decision rules with guard-banding** (aligned with ILAC G8 and ISO 14253-1).

Most calibration labs are currently updating their Excel templates and uncertainty calculation workflows to match. This MCP server ships these primitives end-to-end and is designed to plug directly into the lab's chat-based AI workflow. The prior-art search below found no equivalent, but that is an absence of evidence, not proof of uniqueness. See [Issue #6](https://github.com/kyb8801/measurement-uncertainty-mcp/issues/6) for a planned KOLAS / A2LA / UKAS certificate auto-generation feature.

## What this server does

Exposes 10 MCP tools that implement the **Guide to the Expression of Uncertainty in Measurement (GUM, JCGM 100:2008)** and its **Monte Carlo supplement (JCGM 101:2008)**:

| Tool | What it returns |
|---|---|
| `type_a_uncertainty` | Statistical uncertainty from a sample (n, mean, std, standard uncertainty, dof) |
| `type_b_rectangular` | Non-statistical uncertainty from a known half-width, uniform distribution (u = half_width / √3) |
| `type_b_triangular` | Same for triangular distribution (u = half_width / √6) |
| `type_b_normal` | Non-statistical uncertainty from a k-expanded value (u = U / k) |
| `combine_uncertainty` | Combined standard uncertainty from a list of components and sensitivities |
| `welch_satterthwaite` | Effective degrees of freedom from components |
| `expanded_uncertainty` | Expanded uncertainty with coverage factor k for a target confidence level |
| `monte_carlo_propagate` | **JCGM 101 Monte Carlo propagation** — output mean, standard uncertainty, shortest coverage interval, skewness, excess kurtosis. Use when the model is non-linear, inputs are non-Gaussian, or ν_eff is too small for k=2 to be valid |
| `list_uncertainty_templates` | Catalog of pre-built uncertainty budgets (CMM length, CD-SEM CD, DMM voltage, thermocouple, balance, OCD film thickness). Filters by industry / measurand |
| `apply_uncertainty_template` | Run a named template end-to-end — combine components, compute ν_eff, report U at target confidence. Accepts an `overrides` map so a template adapts to your setup without copy-paste |

The Python library also ships a `propagate(formula, estimates, components)` helper for numerical uncertainty propagation through an arbitrary callable — not exposed as an MCP tool because callables don't serialize over JSON, but directly importable from `measurement_uncertainty_mcp.math_kernel`.

## Who this is for

- **Semiconductor equipment engineers** doing CD-SEM, OCD, TEM, AFM, optical metrology. Wafer dispositions with proper uncertainty budgets, not hand-waved error bars.
- **Calibration labs** (KOLAS, A2LA, UKAS) that need uncertainty budgets in every certificate and spend hours in Excel on the same formulas.
- **AI engineers building quality-control agents** that must reason about measurement uncertainty before making a pass/fail call.
- **Research groups** publishing in journals that require GUM-compliant uncertainty reporting (AIP, IOP, Elsevier metrology titles).

## Five example queries (paste these into Claude Desktop)

After connecting the server, you can ask things like:

1. **CMM length calibration at 10 mm nominal**
   > "Apply the `cmm_length_10mm` template with my repeatability of 0.0003 mm from 10 readings. Report u_c and U at 95% confidence."

2. **CD-SEM 45 nm linewidth uncertainty budget**
   > "Type A from these 20 CD-SEM measurements: [45.12, 45.08, 45.15, ... nm]. Combine with magnification calibration ±0.5 nm at k=2 and line-edge roughness ±0.4 nm at k=2. Report ν_eff via Welch-Satterthwaite."

3. **DMM 10 V calibration with TUR check**
   > "Reference standard ±20 µV at k=2, DMM resolution half-width 1 µV, repeatability 3 µV from n=20. Compute u_c, expanded U at 95%, and the TUR if my tolerance is ±100 µV."

4. **Type-K thermocouple at 100 °C, classroom budget**
   > "Apply `thermocouple_k_100c` template, override `dmm_voltage` to ±0.05 °C at k=2. What is the dominant uncertainty contributor?"

5. **Non-linear ratio model — Monte Carlo propagation**
   > "Compute Y = (V × R) / (V + I) where V ~ N(10, 0.05), R ~ N(100, 0.5), I ~ N(0.1, 0.001). Run Monte Carlo with 200k trials and report the shortest 95% coverage interval."

## Hosted endpoint

A hosted instance runs on MCPize for MCP clients that cannot run Python locally (sign-in required). Self-hosting from this repository gives the same tools.

## Quickstart — hosted (no install)

Connect your MCP client directly to the live Cloud Run endpoint via MCPize. No Python, no dependencies, no config.

### Claude Desktop / Cursor / Windsurf / Cline (one-line)

```bash
npx -y mcpize connect @kyb8801/measurement-uncertainty --client claude
```

Replace `--client claude` with `cursor`, `windsurf`, or `cline` as needed.

### Claude Code CLI

```bash
claude mcp add --transport http "Measurement Uncertainty" https://measurement-uncertainty.mcpize.run
```

### Manual config (`claude_desktop_config.json`)

```json
{
  "mcpServers": {
    "Measurement Uncertainty": {
      "url": "https://measurement-uncertainty.mcpize.run"
    }
  }
}
```

## Quickstart — local install (60 seconds)

For airgapped labs, offline use, or if you'd rather run locally:

```bash
# 1. Clone and install
git clone https://github.com/kyb8801/measurement-uncertainty-mcp.git
cd measurement-uncertainty-mcp
pip install -e .

# 2. Run the stdio server (will connect to any MCP client)
measurement-uncertainty-mcp
```

Then add this to `~/Library/Application Support/Claude/claude_desktop_config.json`
(macOS) or `%APPDATA%\Claude\claude_desktop_config.json` (Windows):

```json
{
  "mcpServers": {
    "measurement-uncertainty": {
      "command": "python",
      "args": ["-m", "measurement_uncertainty_mcp"]
    }
  }
}
```

Restart Claude Desktop, then ask:

> "Compute the Type A uncertainty for these 10 CD-SEM measurements: 45.12, 45.08, 45.15, 45.11, 45.09, 45.13, 45.10, 45.14, 45.07, 45.12 nm. Report u, ν, and the expanded uncertainty at k=2."

## Uncertainty-budget templates

Six starter templates ship in v0.2, covering the most commonly recurring budgets in calibration, teaching, and fab metrology:

| Template id | Industry | Measurand | Nominal |
|---|---|---|---|
| `cmm_length_10mm` | calibration_lab | length | 10 mm |
| `dmm_dc_voltage_10v` | calibration_lab | voltage | 10 V |
| `cdsem_linewidth_45nm` | semiconductor | length | 45 nm |
| `ocd_film_thickness_50nm` | semiconductor | thickness | 50 nm |
| `thermocouple_k_100c` | university | temperature | 100 °C |
| `analytical_balance_500g` | university | mass | 500 g |

`list_uncertainty_templates` previews component names, descriptions, and references. `apply_uncertainty_template` reads the raw component numbers, combines them via the GUM chain, and returns `U` at the target confidence. Users can pass an `overrides` map keyed by component name to adapt a template to their own measurement setup.

When self-hosting, set `MCP_TIER=team` in the server environment to enable `apply_*`.

## Status

- [x] Server skeleton
- [x] Tool definitions (10 tools, JSON Schema)
- [x] Math kernel
- [x] MCPize deployment (live at `measurement-uncertainty.mcpize.run`, 2026-04-22)
- [x] Public beta — 10 tools discovered and callable
- [x] Cold-start optimization: scipy lazy import, cold p50 ~9× faster (#4)
- [x] Monte Carlo uncertainty propagation (GUM Supplement 1 / JCGM 101:2008, 2026-04-22) (#2)
- [x] Uncertainty-budget template library v1 — 6 seed templates (#3, 2026-04-23)
- [ ] Template library expansion: target 20 templates (pressure, torque, flow, dimensional, electrical)

## Differentiation

Searched mcp.so, Smithery, and MCPize on 2026-04-17 for: `uncertainty`, `metrology`, `calibration`, `GUM`, `measurement`. **Zero results** on that date, in those registries, for those terms. That is the whole claim — it does not establish that no such server exists anywhere, and no market-size estimate is offered here.

## Testing

```bash
pytest tests/        # kernel + monte carlo + templates — all 44 tests should pass
```

## License

MIT — see [LICENSE](LICENSE). Free for commercial use, attribution appreciated.