Event Tree 4
Event Tree 4 : Definition: graphical tool used to illustrate the range and probabilities of possible outcomes that arise from an initiating event. Sample Usage: Analysts used an event tree to diagram possible outcomes from a terrorist attack. Annotation: (1) Event trees use forward logic; they begin with an initiating event and work forward in time to determine the possible outcomes. (2) The probabilities used in event trees are conditional probabilities because they are based on the assumption that the initiating event has already occurred. (See Probability annotation for a description of conditional probability). (3) As an example, consider Figure A. The initiating event is an Attack Attempted. From the initiating event, the tree branches into a sequence of random variables, called events. The branching point at which a new random event is introduced is called a node and is depicted by a circle. The first of these random events is Personnel Action to Stop Attack. The Personnel Action to Stop Attack is successful with probability 1-P1 and fails to stop the attack with probability P1. If Personnel Action to Stop Attack is successful, then the branch leads to the final outcome of Unsuccessful Attack, No Damage (Scenario A). If Personnel Action to Stop Attack is not successful, then the branch leads to the next node representing the random event of whether the Security Equipment to Stop Attack is successful or not with probabilities of 1-P2 and P2 respectively. If the Security Equipment to Stop Attack is successful then the branch leads to the final outcome of Unsuccessful Attack, No Damage (Scenario B). If Security Equipment to Stop Attack fails then the branch leads to the final outcome of Successful Attack, Damage to System (Scenario C). Assuming that P1 equals 10% or 0.1 and P2 equals 30% or 0.3, then the conditional probabilities of a Successful and Unsuccessful Attack, given that the initiating event occurs and an attack is attempted, are calculated as follows: Probability of Successful Attack given that an attack is attempted: = Probability of Scenario C = Probability that Personnel Action to Stop Attack fails and Security Equipment to Stop Attack fails. = P1 * P2 = 0.1 * 0.3 = 0.03. Therefore, the conditional probability of a Successful Attack, given the attack is attempted, is 3%. Probability of Unsuccessful Attack given that an attack is attempted: = Probability of Scenario A or Scenario B occurring = Probability that Personnel Action to Stop Attack is successful or Security Equipment to Stop Attack is successful. = (1 - P1) + [P1 * (1 - P2)] = 0.9 + (0.1 * 0.7) = 0.97. Therefore, the conditional probability of an Unsuccessful Attack, given that the attack is attempted, is 97%. Notice that the Probability of Successful Attack plus the probability of Unsuccessful Attack equals one because there are no alternative outcomes. Event trees differ from fault trees by starting with an initiating event and moving forward in time to determine possible final outcomes. Fault trees start with an outcome and work backwards in time to determine the range of events that may have caused the outcome. See Also: fault tree, probability
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