1A BAYESIAN MODEL FOR RARE EVENT RISK ASSESSMENT USING EXPERT JUDGMENT ABOUT PAIRED SCENARIO COMPARISONS P.S. Szwed and J.R. van Dorp Abstract When challenged with understanding complex, technological systems, managers often use analysis to characterize risk. Managers use this information to design projects, develop policy, and allocate resources in order to mitigate system risk. This paper presents a Bayesian risk analysis methodology for combining expert judgment with the manager’s prior system knowledge to allow identification of risk mitigation opportunities. The model is demonstrated through a study of the nation’s largest passenger ferry system and the results compare favorably with previous classical analyses. Hence, this methodology might be useful to engineering managers for rare event risk analysis in other applications and other disciplines as well. 1. Introduction Risk analysis, also known as risk assessment, is widely recognized as a systematic, science-based process for quantitatively (or qualitatively) describing risk. Risk is commonly described as a combination of the likelihood of an undesirable event (accident) occurring and its consequences. Alternatively, in the context of this paper, it can be expressed as a mathematical combination of an accident’s event probability of occurrence and the consequence of that event should it occur (for a detailed discussion of the definition of risk, see Kaplan (1997)). Regardless of exactly how these concepts are defined, however, information about risk is critically important to the decision making process. Engineering managers use the information gained from risk analysis to design projects, develop policy, and allocate resources in their efforts to mitigate system risk. Often, engineering managers are interested in gaining information about rare events, such as catastrophic accidents or system failures. However, rare event risk information inherently suffers from data scarcity. While the consequences of rare events scenarios may be assessed using engineering based scenario analyses, their frequency data are usually unavailable. In such a case, engineering managers may turn to expert judgment to develop frequency data for these low frequency, high consequence events. Expert judgment is an informed assessment or estimate (based on the expert’s training and experience) about an uncertain quantity or quality of interest. An expert is a person who is recognized (by peers, decision makers, or others) for their skills, knowledge, and expertise in a particular domain of interest. When treated properly, expert judgment is an important source of information, particularly for risk analysis (See, for example Cooke, 1991). This paper presents a methodology for engineering managers to incorporate expert judgment as a means of obtaining accident probabilities. Managers can use this risk analysis information for identifying opportunities to mitigate system risk. 2. Mathematical Model In order to make use of the expert judgment elicited from several experts, a mathematical inference model for aggregation and combination becomes necessary. Such a mathematical model is formulated in this paper and will provide a means for combining the decision maker’s prior knowledge with the expert judgment about paired scenario comparisons. 2.1. Accident probability model. When developing probabilities to perform a risk analysis, it is generally desirable to link causal factors to the accident probability. Such models are often referred to as causal models, or accident probability models. A causal model allows for the estimation of annual accident probability under a specific situation, or scenario. Knowing the probability of an accident per year in a specific scenario and predicting ahead the occurrence of such a scenario helps identify which precautionary measures to consider for accident prevention. For example, if it is known that the probability of an accident is unacceptably high for the scenario when three laden tows (each with twelve barges) meet in close proximity (within a half-mile of each other) during a high river stage on the Mississippi River at Algiers Point in New Orleans, then regulating to prevent such a scenario is warranted. The authorities may require vessel masters to provide one-hour advance notice for passage through that point so that traffic advisors can alert them of this potential scenario and they can slow down to avoid traffic that allows such a scenario to happen. Thus, the advantage of a causal accident probability model is that it allows decisions to be made on which measures to take for ensuring the biggest effect on reducing the probability of an accident.2 One word of caution, however, is perhaps appropriate. Consider the probability of an accident during aircraft landing in low visibility at Tucson Airport in Arizona. Without a doubt, the most dangerous situation for landing air traffic is during low visibility. However, if such bad visibility situations hardly ever occurs in Tucson that airport will not get much safer by developing advanced guiding equipment for low visibility situations. Hence, both the accident probability of a particular system state and its rate of incidence are necessary to make decisions on what precautionary measures to implement. The following accident probability model is postulated: ()()XPXAccidentTβexp|Pr0= (1) where XT=(X1,…,Xv) is a vector of v situational (causal) variables describing a scenario, βT=(β1,…,βv) is a parameter vector, and P0 is a base rate probability. The model in Equation (1) has been proposed in several maritime risk assessments (see Roeleven et al. 1995, Merrick et al. 2000, van Dorp et al. 2001) and assumes that accident probability increases (or decreases) exponentially with a situational variable Xi (rather than linearly). Each situational variable Xi is assumed to be a bounded variable that may be discrete or continuous in nature. Without loss of generality, it is assumed that each situational variable Xi is normalized on a scale of [0, 1]. This normalization allows for comparison of the effects between different situational variables on the accident probability via a comparison of the elements of βT. Positive values of βi indicate that the accident probability increases exponentially with Xi and vice versa. Given the model formulation in Equation (1), it follows that P0 may be interpreted as the inherent