Modeling and simulation is playing an increasing role in supporting tough regulatory decisions, which are typically characterized by variabilities and uncertainties in the scenarios, input conditions, failure criteria, model parameters, and even model form. Variability exists when there is a statistically significant database that is fully relevant to the application. Uncertainty, on the other hand, is characterized by some degree of ignorance. A simple algebraic problem was used to illustrate how various risk methodologies address variability and uncertainty in a regulatory context. These traditional risk methodologies include probabilistic methods (including frequensic and Bayesian perspectives) and second-order methods where variabilities and uncertainties are treated separately. Representing uncertainties with (subjective) probability distributions and using probabilistic methods to propagate subjective distributions can lead to results that are not logically consistent with available knowledge and that may not be conservative. The Method of Belief Scales (MBS) is developed as a means to logically aggregate uncertain input information and to propagate that information through the model to a set of results that are scrutable, easily interpretable by the nonexpert, and logically consistent with the available input information. The MBS, particularly in conjunction with sensitivity analyses, has the potential to be more computationally efficient than other risk methodologies. The regulatory language must be tailored to the specific risk methodology if ambiguity and conflict are to be avoided.
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