Fault Tree Analysis (FTA): From Top Event to Minimal Cut Sets
What is FTA?
Fault tree analysis (FTA) decomposes an undesired system event (the top event) top-down into basic causes (bottom events), using logic gates such as AND and OR to describe how events combine, and thereby finds every path that leads to the top event. FTA supports both qualitative analysis (finding minimal cut sets) and quantitative analysis (computing the top event probability) and is the reliability analysis method specified by IEC 61025. It is also used in accident investigation to verify that the cause chain is complete and no intermediate event is missing.
Logic Gates and Minimal Cut Sets
An OR gate fires when any input occurs and an AND gate fires only when all inputs occur together. Reducing the tree to minimal cut sets (bottom-event combinations that cannot be reduced further) shows the system fragility: fewer cut sets and more single-point failures mean a more vulnerable system. The tool generates the cut sets automatically and ranks each cut set contribution to the top event probability, performing the Boolean algebra reduction to avoid manual errors.
Application Scenarios
FTA fits safety-critical systems in aerospace, nuclear power, chemical process safety and automotive functional safety, and supports risk identification in new-system design reviews. It complements FMEA: FMEA works bottom-up while FTA works top-down, and using both cross-validates coverage. In functional safety, FTA is often combined with FMEA and HAZOP in safety analysis reports to satisfy the hazard analysis requirements of IEC 61508.
Outputs and Precautions
The tool outputs the fault tree structure diagram, the minimal cut set list, the top event probability and sensitivity results. Use reliable bottom-event failure rates (for example MIL-HDBK-217 or FIDES data), model common-cause failures explicitly because they significantly raise real probability, and treat probability results as estimates to be combined with engineering judgment. Sensitivity analysis identifies the bottom events with the largest influence on the top event, guiding the prioritization of improvements and redundant design.