Statistical Foundation for Decision Making in Nuclear Safety–Related Problems Using Best Estimate Plus Uncertainty Analyses

The response of a complex physical system is often evaluated by a tolerance interval for a percentile of the distribution of a variable of interest that is estimated by best-estimate codes. This tolerance interval is used as a test statistic to make decisions about the behavior of the system in the context of the specific safety issue. The most common methods to determine such tolerance intervals are order statistics methods leading to the so-called “95/95” level of safety standard. The application of these methods is predicated on the assumption that the simulated responses are identical to those of an actual reactor under the postulated conditions. We present here a novel statistical framework [referred to as EVS (extreme value statistics) methodology], not relying on the above assumption, for deriving tolerance limits involving data selected from a population that is different from the population of interest. Such a situation arises when the unobservable population is being estimated by an imperfect code and imperfect input. This leads us to distinguishing between “true” system stochastic (aleatory) variables and those resulting from the safety codes (subject to epistemic uncertainty). Methods using Monte Carlo sampling or sensitivity analysis, order statistics, and EVS methods produce different solutions as a consequence of a difference in how the true values and data are distinguished. This difference ultimately leads to different test statistics that are used to solve a decision-making problem. Closed-form expressions for the EVS-based tolerance limits are derived for a large class of models representing complex systems. Problems, both analytical and using actual reactor operating data, are presented and solved. EVS results demonstrate substantial improvements in operational and safety margins when compared to results obtained from existing methods used in the nuclear industry.