Logic Trees: Fault, Success, Attack, Event, Probability, and Decision Trees

Abstract

Abstract This article describes the fundamentals of logic trees used in decision and risk analysis. We include in the broad definition of logic trees any conceptual or mathematical model that describes scenarios of events and/or decisions in a treelike structure. Logic trees are important tools for analyzing uncertain events, defining accident scenarios, assessing risk, calculating joint probability distributions, and evaluating decision options. Six types of logic trees are described, compared, and illustrated in this article: fault trees, success trees, attack trees, event trees, probability trees, and decision trees. Fault trees deductively model the combination of system failures and human errors that could lead to an accident. Success trees are the complement of fault trees and model the combination of events that lead to success. Attack trees model the sequential actions of an intelligent adversary to defeat a defensive system. Event trees inductively model the sequences of events that lead to an accident. Probability trees model a sequence of uncertain events in order to calculate the probability of events in the outcome space. Decision trees are logic trees that include sequential decisions in addition to sequential uncertain events. Examples are provided in this article to illustrate the similarities and differences among the types of logic trees. We conclude with challenges for applying logic trees to homeland security applications.