Probabilistic Risk Analysis Versus Decision Analysis: Similarities, Differences and Illustrations

Abstract

The methods of engineering probabilistic risk analysis and expected-utility decision analysis share a common core: a probabilistic model of occurrences of uncertain events. This model is based on systems analysis and on the identification of an exhaustive and mutually exclusive set of scenarios, their probabilities and their consequences. Both methods rely on an assumption of rationality and the use of Bayesian probability, and both assume separation of probability assessments and of preferences among scenarios’ outcomes. The major differences are rooted in the nature and the framing of the problems that they address. A risk analysis is often performed before decisions have been fully defined, and one of its objectives is then to identify and characterize risk mitigation options. Furthermore, at the time of the analysis, the decision maker who will eventually use the results is often unknown. Therefore, the definition of Bayesian probability as a degree of belief has to be adapted, for instance, by assuming implicit delegation of the user’s judgment to the analyst and the experts, which requires special care in the presentation of the results. Also, a risk analysis is often performed for a single system (e.g., one aircraft) for one unit of time or operation (e.g., one takeoff and landing cycle) when in reality, the analysis may be intended to support risk management decisions that will eventually concern an unknown number of similar systems for an unspecified number of time units. This multiplicity has implications for the treatment of second-level uncertainties (about failure probabilities) and for the need to display these uncertainties in the results. In this paper, the two classical definitions of probability (Bayesian and frequentist) are discussed, focusing on their relevance to both probabilistic risk analysis and decision analysis, when facing aleatory uncertainties (randomness) as well as epistemic uncertainties (limited knowledge about a fundamental phenomenon of interest). The risk and decision analysis methods are then briefly described, along with their similarities and differences. Two illustrations are presented: an analysis, performed in 1990, of the risk of losing a NASA orbiter and its crew due to a failure of the tiles of the thermal protection system, and a method of assessment of the risk of a terrorist attack on the United States in a given time frame, based on available intelligence information (a 2002 study). The latter involves the use of a simple analysis of a game involving alternating decisions and moves by terrorists and the US using a rational model in the descriptive mode. The main conclusion is that whereas the role of the decision analyst is to represent faithfully the beliefs and preferences of a known decision maker in order to identify the preferred alternative, the risk analyst needs to be scrupulous in presenting the model assumptions, as well as the sources and the methods of data processing to allow future decision makers to exercise their own judgments when using the results.