Uncertainties and reliability theories for reactor safety

What makes the safety problem of nuclear reactors particularly challenging is the demand for high levels of reliability and the limitation of statistical information. The latter is an unfortunate circumstance, which forces deductive theories of reliability to use models and parameter values with weak factual support. The uncertainty about probabilistic models and parameters which are inferred from limited statistical evidence can be quantified and incorporated rationally into inductive theories of reliability. In such theories, the starting point is the information actually available, as opposed to an estimated probabilistic model. But, while the necessity of introducing inductive uncertainty into reliability theories has been recognized by many authors, no satisfactory inductive theory is presently available. The paper presents: a classification of uncertainties and of reliability models for reactor safety; a general methodology to include these uncertainties into reliability analysis; a discussion about the relative advantages and the limitations of various reliability theories (specifically, of inductive and deductive, parametric and nonparametric, second-moment and full-distribution theories). For example, it is shown that second-moment theories, which were originally suggested to cope with the scarcity of data, and which have been proposed recently for the safety analysis of secondary containment vessels, are the least capable of incorporating statistical uncertainty. The focus is on reliability models for external threats (seismic accelerations and tornadoes). As an application example, the effect of statistical uncertainty on seismic risk is studied using parametric full-distribution models