The Nature and Role of True Value in Monte Carlo Uncertainty Analyses with Application to BEAU Methodology

Abstract

The current best estimate and uncertainty analysis (BEAU) methodology for LOCA safety analysis requires as input probability distributions for the relevant process variables as well as their associated uncertainties. In particular, among these process variables are maximum channel and bundle powers including their uncertainties. Upon deeper consideration it becomes apparent that it is not possible to satisfy the requirement in a straightforward manner. The reason for this is that the mathematical notion of the variables in the compliance with channel/bundle power licence limit analysis (the CU approach) are conceptually different. A crucial difference between the two approaches is that the CU analysis considers the error in the simulated variable, estimated by a Monte Carlo procedure, while BEAU analysis does not. The Monte Carlo procedure of the current BEAU analysis lacks a formal description of its fundamentals and treatment of the uncertainties, while the CU methodology provides a rigorous mathematical framework for the simulation of variables, its meaning and the associated uncertainty analyses. Using this mathematical framework, it is shown how to understand the BEAU simulation, what the input process variables should be and how the input errors should be treated. The result of a BEAU analysis is an extreme value, such as a maximum fuel sheath temper- ature, and hence the crucial statistical properties of such a result depend on the understanding of the extreme value statistics. The current BEAU analysis may suffer from the lack of consideration for the extreme value statistics. In this paper some examples are provided to demonstrate the effect of the extreme value statistics on the final result of the desired computation. It is also argued that the CU approach applied in BEAU analysis leads to estimates for the simulated variables with well defined statistical properties. Moreover, such an approach may lead to more favourable results than the current BEAU analysis in a sense that the former may produce results with larger operating margins.