Probabilistic risk assessment (PRA) provides practical techniques for predicting and managing risks (i.e., frequencies and severities of adverse consequences) in many complex engineered systems. In this chapter, we survey methods for PRA and decision making in engineered systems, emphasizing progress in methods for dealing with uncertainties (e.g., via Bayesian belief networks, with dependencies among inputs expressed via copulas), communicating results effectively, and using the results to guide improved decision making by multiple parties (e.g., teams of stakeholders). For systems operating under threats from intelligent adversaries, novel methods (e.g., game-theoretic ideas) can help to identify effective risk-reduction strategies and resource allocations. The focus on methodology reflects the belief of the authors that in hard decision problems, where the risks and the best courses of action are unclear (often because of sparse, ambiguous, or conflicting data), state-of-the-art methodology may be critical to good risk management. This chapter discusses some of the most useful current methodologies, and suggests possible directions for extensions and improvements.

GUILDENSTERN: We have been spinning coins together since I don't know when, and in all that time … I don't suppose either of us was more than a couple of gold pieces up or down. I hope that doesn't sound surprising because its very unsurprisingness is something I am trying to keep hold of. The equanimity of your average tosser of coins depends upon a law, or rather a tendency, or let us say a probability, or at any rate a mathematically calculable chance, which ensures that he will not upset himself by losing too much nor upset his opponent by winning too often. This made for a kind of harmony and a kind of confidence. It related the fortuitous and the ordained into a reassuring union which we recognized as nature. The sun came up about as often as it went down, in the long run, and a coin showed heads about as often as it showed tails. Then a messenger arrived. We had been sent for … Ninety-two coins spun consecutively have come down heads ninety-two consecutive times.