faulttree

Fault tree analysis (FTA) is a top-down, deductive failure analysis in which a defined undesired state of a system, known as the top event, is analyzed using Boolean logic to identify the combinations of lower-level events that could cause it. The method is used to understand how failures propagate and to support safety, reliability, and risk assessment activities.

A fault tree is built from basic events, which are failures with no further decomposition, and from intermediate events that are derived from combining other events. The logical relationships are represented by gates, most commonly OR and AND. An OR gate indicates that any input can cause the output, while an AND gate requires all inputs to occur. Other gates, such as NOT, XOR, and various k-out-of-n configurations, may be used to model more complex relationships. The structure typically culminates in a single top event that characterizes the undesired outcome.

Quantitative use of FTA involves assigning probabilities to basic events and computing the probability of the top event through the gate logic. This often yields minimal cut sets—the smallest combinations of basic events that lead to the top event. FTA supports qualitative insights, such as identifying critical components and potential failure paths, and quantitative analyses, such as estimating risk and identifying design weaknesses. Data quality and the assumption of independence among basic events are common limitations.

FTA originated in the 1960s and has been widely applied in safety-critical industries, including aerospace, nuclear power, and chemical processing. It is often used in conjunction with event tree analysis and reliability block diagrams as part of a larger probabilistic risk assessment toolkit.