How do I install the Uncertainty Propagation skill?

Run npx skillmds@latest add ashfordeou/uncertainty-propagation in your terminal (requires Node.js), paste this page's agent-chat prompt into Claude, Cursor, or any MCP-connected agent, or download the SKILL.md file and copy it into your agent's skills directory.

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Is Uncertainty Propagation free to use?

Yes. Installing skills from SkillMD is free. This skill is licensed under Apache-2.

Who published Uncertainty Propagation?

ashfordeOU (@ashfordeou) published this skill. Their other Agent Skills are listed on their SkillMD profile.

Uncertainty Propagation by ashfordeou

Name: Uncertainty Propagation
Author: ashfordeOU

Uncertainty Propagation

Use when you must propagate measurement uncertainties through a calculation with the GUM first order law: combine the sensitivity coefficients and standard uncertainties of the independent inputs into the combined standard uncertainty, expand it with a coverage factor, and identify the dominant contribution. Produces the combined standard uncertainty, the expanded uncertainty, and the per input variance shares that gate the measurement uncertainty budget. Trigger: uncertainty propagation, combined standard uncertainty, expanded uncertainty, coverage factor, sensitivity coefficient, GUM, variance contribution, dominant uncertainty.

ashfordeOU Updated Sep 17, 2026

File contents

Uncertainty Propagation (cross-cutting/numerics/uncertainty-propagation)

Use when the task is propagating measurement uncertainties through a calculation with the GUM first order law: combined standard uncertainty, expanded uncertainty, and the dominant variance contribution.

Domain quick reference

Input i has sensitivity coefficient s_i = df/dx_i at the operating point and standard uncertainty u_i (one sigma).
The GUM first order law for independent inputs gives the combined standard uncertainty u_c = sqrt(sum_i (s_i * u_i)**2); the term (s_i * u_i)**2 is the variance contribution of input i.
The expanded uncertainty is U = k * u_c with coverage factor k, 2.0 by convention (roughly 95 percent coverage for a normal distribution).
The percent share of input i is 100 * (s_i * u_i)2 / u_c2; shares sum to 100.
The first order law assumes independent inputs; correlated inputs need the full covariance form, which this logic does not implement.

Workflow

Collect the sensitivity coefficients and standard uncertainties for each independent input.
Combine them with combined_standard_uncertainty(sensitivities, uncertainties).
Expand with expanded_uncertainty(combined, k=2.0).
Rank the contributors with uncertainty_contributions(...) and report the dominant one with dominant_contribution(...) before gating the uncertainty budget.

Pitfalls

Applying the first order law to correlated inputs: the independent sum underestimates or overestimates the combined uncertainty; the covariance form is required.
Negative uncertainties: physically meaningless; the logic raises ValueError.
Mixing unit systems: sensitivities and uncertainties must share a consistent unit system; no conversion is performed.
Using a non-positive coverage factor: the logic raises ValueError.
Reporting the largest sensitivity instead of the largest variance contribution: the contribution weights the sensitivity by the uncertainty, so ranking by contribution is the correct ordering.

Behavior contract (gate 3)

The propagation, expansion, and contribution logic is exercised by the gate 3 contract test: scripts/test_uncertainty_propagation.py against scripts/uncertainty_propagation_logic.py (stdlib unittest, offline). Run:

python3 scripts/test_uncertainty_propagation.py

Compliance

NACA Report 824 is US government work (public domain); the pack anchor per standards-map.yaml. The GUM (JCGM 100) first order law is generic measurement methodology, not RTCA or SAE content; summary and formulas only.
compliance: STANDARDS-REF, gated: false.

---name: uncertainty-propagationdescription: Use when you must propagate measurement uncertainties through a calculation with the GUM first order law: combine the sensitivity coefficients and standard uncertainties of the independent inputs into the combined standard uncertainty, expand it with a coverage factor, and identify the dominant contribution. Produces the combined standard uncertainty, the expanded uncertainty, and the per input variance shares that gate the measurement uncertainty budget. Trigger: uncertainty propagation, combined standard uncertainty, expanded uncertainty, coverage factor, sensitivity coefficient, GUM, variance contribution, dominant uncertainty.license: Apache-2.0---# Uncertainty Propagation (cross-cutting/numerics/uncertainty-propagation)Use when the task is propagating measurement uncertainties through acalculation with the GUM first order law: combined standarduncertainty, expanded uncertainty, and the dominant variancecontribution.## Domain quick reference- Input i has sensitivity coefficient s_i = df/dx_i at the operating point and standard uncertainty u_i (one sigma).- The GUM first order law for independent inputs gives the combined standard uncertainty u_c = sqrt(sum_i (s_i * u_i)**2); the term (s_i * u_i)**2 is the variance contribution of input i.- The expanded uncertainty is U = k * u_c with coverage factor k, 2.0 by convention (roughly 95 percent coverage for a normal distribution).- The percent share of input i is 100 * (s_i * u_i)**2 / u_c**2; shares sum to 100.- The first order law assumes independent inputs; correlated inputs need the full covariance form, which this logic does not implement.## Workflow1. Collect the sensitivity coefficients and standard uncertainties for each independent input.2. Combine them with combined_standard_uncertainty(sensitivities, uncertainties).3. Expand with expanded_uncertainty(combined, k=2.0).4. Rank the contributors with uncertainty_contributions(...) and report the dominant one with dominant_contribution(...) before gating the uncertainty budget.## Pitfalls- Applying the first order law to correlated inputs: the independent sum underestimates or overestimates the combined uncertainty; the covariance form is required.- Negative uncertainties: physically meaningless; the logic raises ValueError.- Mixing unit systems: sensitivities and uncertainties must share a consistent unit system; no conversion is performed.- Using a non-positive coverage factor: the logic raises ValueError.- Reporting the largest sensitivity instead of the largest variance contribution: the contribution weights the sensitivity by the uncertainty, so ranking by contribution is the correct ordering.## Behavior contract (gate 3)The propagation, expansion, and contribution logic is exercised bythe gate 3 contract test: scripts/test_uncertainty_propagation.pyagainst scripts/uncertainty_propagation_logic.py (stdlib unittest,offline). Run:python3 scripts/test_uncertainty_propagation.py## Compliance- NACA Report 824 is US government work (public domain); the pack anchor per standards-map.yaml. The GUM (JCGM 100) first order law is generic measurement methodology, not RTCA or SAE content; summary and formulas only.- compliance: STANDARDS-REF, gated: false.

Frequently asked questions