Generalized extreme value analysis of efficient evaluation of extreme values in random media criticality calculations

The uncertainty of fuel debris criticality can be estimated by Monte Carlo criticality calculations repeated over independent replicas of some properly modelled random medium. Incomplete randomized Weierstrass function (IRWF) is a modelling framework for such calculations. Under these approaches at hand, the theme of this paper is how to efficiently analyse extreme realizations of neutron effective multiplication factor (keff) over IRWF random media replicas. To this end, a new bounded amplification (BA) technique is applied to IRWF. The numerical results clearly indicate that the BA-applied IRWF reduces a required number of random media replicas at least by an order of magnitude. To rigorously validate this efficiency gain, generalized extreme value (GEV) analysis is applied to a data set of keff values obtained without applying BA. It turns out that the extreme values of these keff values follow the Weibull distribution. Therefore, the theory of GEV guarantees the existence of an upper limit for these keff values, and the actually computed upper limit is indeed smaller than or equal to the top two keff values obtained from an order-of-magnitude reduced number of BA-applied IRWF random media replicas. This means that the efficiency gain brought by BA has been confirmed by the GEV methodology. In addition, a method of rejecting spurious estimation values due to statistical fluctuation is demonstrated concerning the extreme value index in the GEV analysis.