Numerical experiments on order statistics method based on Wilks' formula for best-estimate plus uncertainty methodology

Abstract

The best-estimate plus uncertainty method has been widely used in safety analysis for nuclear power plants. In this method, it is very important to have a sound uncertainty propagation method which should model the propagation of both epistemic and aleatory uncertainties and provide clear interpretation of the result. A typical example of such methods for nuclear application is the order statistics method based on Wilks' formula. This method requires practically small number of simulations to obtain the desired tolerance limit and the number is independent of the number of uncertainty parameters. In addition, since the method is based on non-parametric statistics, the conclusions drawn by the method should have distribution-free characteristics. This study aims at assessing the characteristics of the order statistics method based on Wilks' formula by means of numerical experiments and focuses on one-sided test which is typically used for safety evaluation. The distribution-free characteristics have been assessed by using 21 trial distributions and fully random samples out of all trial distributions. The effect of the order of Wilks' formula on the estimated tolerance limit is investigated by examining the characteristics of the results from various orders. The analysis results clearly confirm the order-free and distribution-free characteristics of the tolerance limit estimated by the order statics method based on Wilks' formula. In addition, it is found that the application of higher-order Wilks' formula is recommended in order to achieve less conservative and sensitive tolerance limit.