Reliability Sensitivity Example

A worked example identifying which input uncertainties contribute most to the failure probability using sensitivity analysis.

Probabilistic & Reliability5 min read

worked examplesensitivityreliabilityvariance contributionimportance

Problem

A structural component has two uncertain inputs: load (CoV = 15%) and strength (CoV = 8%). The limit state is g = strength - load. Which input contributes more to the failure probability?

Given

Load: mean 200, CoV 15% → sigma = 30
Strength: mean 350, CoV 8% → sigma = 28
g = strength - load
Both normally distributed, independent

Solution

Variance of g:
sigma_g^2 = sigma_strength^2 + sigma_load^2
          = 28^2 + 30^2
          = 784 + 900 = 1684

Variance contribution:
Load:     900/1684 = 53.4%
Strength: 784/1684 = 46.6%

The load contributes 53.4% of the output variance — it is the
dominant source of uncertainty in the reliability estimate.

Interpretation

The load uncertainty contributes slightly more to the failure probability than the strength uncertainty. To reduce the failure probability most effectively, the load uncertainty should be reduced first — through better load characterisation or more operational data. This is an illustrative example.