Question 1

Why do GUM and Monte Carlo give different uncertainty estimates?

Accepted Answer

The GUM method uses a first-order Taylor expansion (linear approximation) of the output function. For strongly nonlinear formulas, this under- or over-estimates uncertainty. Monte Carlo directly samples all input combinations and captures nonlinear effects. When the relative difference between GUM and Monte Carlo standard deviations exceeds about 10%, the formula has significant nonlinearity and the Monte Carlo result is more reliable.

Question 2

Once I identify the dominant variable in the tornado chart, what should I do?

Accepted Answer

The variable with the largest |∂f/∂xᵢ · uᵢ| bar contributes most to output uncertainty. To reduce total output uncertainty efficiently, prioritize improving measurement accuracy, tighter tolerances, or better calibration for that variable. Improving lower-ranked variables yields diminishing returns. For example, if load F dominates in the stress formula σ = F/(b·h), invest in a more accurate load cell rather than improving dimensional measurements.

Question 3

How many Monte Carlo samples do I need for reliable results?

Accepted Answer

For the standard deviation σ, 10,000 samples gives approximately 1% relative statistical error. For the 95th percentile, 10,000 samples is adequate. For the 99th percentile or extreme tail behavior (e.g., failure probability), at least 100,000 samples are recommended. The default value of 10,000 in this tool is appropriate for typical engineering uncertainty quantification tasks.

Question 4

Why does the fatigue exponent m often dominate uncertainty in the fatigue life formula?

Accepted Answer

In the fatigue life formula N = (S/σ)^m, the exponent m amplifies uncertainty multiplicatively via ∂N/∂m = N·ln(S/σ). For S/σ = 1.5 and m = 3.5, a 1% uncertainty in m produces ln(1.5) ≈ 40.5% relative uncertainty in N. Experimental S-N curves typically show ±5–15% scatter in m, which directly translates to large life prediction uncertainty. Reducing m uncertainty through more S-N data points is the most effective way to improve fatigue life prediction confidence.

Uncertainty Propagation & Monte Carlo Analysis

Formula Selection

Input Variable Uncertainties

Monte Carlo Settings

Monte Carlo Output Distribution Histogram

Tornado Chart (Sensitivity Analysis)

Most Sensitive Variable vs Output (Scatter)