A conceptual model for the organization and execution of a performance assessment of a radioactive waste disposal site, including uncertainty and sensitivity analysis, is described. This model is based on a formal definition of risk as a collection of ordered triples, where the first element in each triple is a set of similar occurrences (i.e., a scenario), the second element is the probability or frequency of the first element, and the third element is a vector of consequences associated with the first element. This division of risk into its three constituent parts provides a useful model for the structure of a performance assessment for several reasons. First, it provides a clear distinction between the major parts of a performance assessment, which are determining what can happen, determining how likely things are to happen, and determining what the consequences of specific events are. Second, it provides a way to distinguish between different types of uncertainty, including completeness, aggregation, model selection, imprecisely known variables, and stochastic variation. Third, it leads naturally to the representation of stochastic variation with a complementary cumulative distribution function (CCDF) and the representation of state of knowledge uncertainty with a family or distribution of CCDFs. Fourth, it provides a context in which the U.S. Environmental Protection Agency limits for radioactive releases to the accessible environment can be represented and calculated. Fifth, it facilitates relating the development of scenarios and their probabilities to the concepts used in formal probability theory. The preceding ideas are illustrated with results obtained in a preliminary performance assessment for the Waste Isolation Pilot Plant in southeastern New Mexico.