A quantitative definition of risk is suggested in terms of the idea of a "set of triplets." The definition is extended to include uncertainty and completeness, and the use of Bayes' theorem is described in this connection. The definition is used to discuss the notions of "relative risk," "relativity of risk," and "acceptability of risk."

A point of view is suggested from which the Hierarchical Holographic Modeling (HHM) method can be seen as one more method within the Theory of Scenario Structuring (TSS), which is that part of Quantitative Risk Assessment having to do with the task of identifying the set of risk scenarios. Seen in this way, HHM brings strongly to our attention the fact that different methods within TSS can result in different sets of risk scenarios for the same underlying problem. Although this is not a problem practically, it is a bit awkward conceptually from the standpoint of the "set of triplets" definition of risk, in which the scenario set is part of the definition. Accordingly, the present article suggests a refinement to the set of triplets definition, which removes the specific set of scenarios, found by any of the TSS methods, from the definition of risk and casts it, instead, as an approximation to the "true" set of scenarios that is native to the problem at hand and not affected by the TSS method used.

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During the period from 1977 to 1984, Pickard, Lowe and Garrick, Inc., had the lead in preparing several full scope probabilistic risk assessments for electric utilities. Five of those studies are discussed from the point of view of advancements and lessons learned. The objective and trend of these studies is toward utilization of the risk models by the plant owners as risk management tools. Advancements that have been made are in presentation and documentation of the PRAs, generation of more understandable plant level information, and improvements in methodology to facilitate technology transfer. Specific areas of advancement are in the treatment of such issues as dependent failures, human interaction, and the uncertainty in the source term. Lessons learned cover a wide spectrum and include the importance of plant specific models for meaningful risk management, the role of external events in risk, the sensitivity of contributors to choice of risk index, and the very important finding that the public risk is extremely small. The future direction of PRA is to establish less dependence on experts for in-plant application. Computerizing the PRAs such that they can be accessed on line and interactively is the key.