Sensitivity Analysis with Fault Tree Analysis — FTA-SA

Birnbaum importance is the partial derivative of the top-event probability with respect to a basic event's probability — it measures how structurally sensitive the system is to that event, regardless of its actual probability. Risk Reduction Worth (RRW) is the ratio of the current top-event probability to what it would be if that event were made perfectly reliable (probability = 0). RRW is more operationally useful because it accounts for the event's actual probability and tells you directly how much risk you could eliminate by fixing that component.

Use global sensitivity analysis (e.g., Sobol variance decomposition or Morris screening) when basic event probabilities are uncertain over wide ranges, when the fault tree contains non-linear interactions (AND gates with multiple inputs create multiplicative terms), or when you suspect that common-cause failures make events correlated. One-at-a-time variation is computationally cheaper and interpretable but can miss interaction effects that shift which event is truly most critical.

Yes, but with caution. Hardware component failure rates have established databases; software failure probabilities are harder to quantify and depend heavily on operational profile and defect density. In practice, FTA is applied to software-hardware systems by treating software as a basic event with an estimated failure-on-demand probability derived from testing or industry benchmarks. The sensitivity analysis then reveals how sensitive overall system risk is to uncertainty in those software failure probability estimates.

Common sources include MIL-HDBK-217 (electronic components), OREDA (offshore reliability data), IEEE Std 493 (electrical systems), NUREG/CR-6928 (nuclear component performance), and SINTEF industrial reliability databases. Where generic data are unavailable, Bayesian updating with plant-specific evidence or expert elicitation using structured expert judgement protocols is standard practice.

PRA is a broader framework that uses multiple tools — fault trees, event trees, common-cause failure models, and human reliability analysis — to quantify risk across many accident sequences. FTA-SA is one core component within a PRA: the fault trees model how each top event (e.g., loss of coolant) can occur, and sensitivity analysis on those trees identifies which failure probabilities most drive risk. Full PRA integrates the fault tree results with event tree frequencies and consequence analysis.