An Introduction to Probabilistic Risk Analysis for Engineered Systems

Abstract The risk of failure of a system can sometimes be simply characterized by the probability of system failure per time unit or operation. More often, it include both the probabilities and the consequences of the different failure scenarios, in which case the risk can be described by the probability distribution of the losses in a given time frame. Risk management, in turn, involves finding and fixing a system's weaknesses by asking the following questions. How does it work? How can it fail? What can be done about it given that we are not infinitely rich and time is limited? For a complex engineered system, one may not have a sufficient statistical database to assess a failure probability at the system level. In that case, one can use systems analysis and Bayesian probability to assess the risk. Probabilistic risk analysis (PRA) has been developed in engineering, in particular in the nuclear power industry to quantify the risk of system failures. The method relies in part on event trees and fault trees, or, similarly, on Bayesian networks. It involves first, identification of failure scenarios, then computation of their probabilities by combining the probabilities of events and the distributions of random variables involved, accounting for dependencies and rare occurrences. The next step is the evalution of the consequences of the failure scenarios. The results can then be used as input into a risk management problem with two objectives: to optimize resource allocation (e.g., to minimize the probability of system failure given budget and system failure given budget and schedule constraints) and to check that in the end the failure risk is tolerable. This article describes and illustrates the PRA method and some of its extensions.