Numerical experiment to evaluating two-sided tolerance limit for safety analysis

Abstract

Uncertainty analysis is required to quantify uncertainties in safety evaluation for industrial applications when the best-estimate methodology is employed. The nonparametric order statics method suggested by the GRS (Gesellschaftfür Anlagen-und Reaktorsicherheit) is one of the uncertainty evaluation methodologies to obtain the figure of merits with a probability of 95 % and confidence of 95 %, namely 95/95 value. In this method, the number of repeated calculations with perturbation to acquire the 95/95 value is decided by a formula suggested by Wilks and is dependent on the number of uncertainty parameters. Thus, the method is effective when the reference system has a large number of parameters which bring uncertainty in the analysis. Previous studies indicate that the method can estimate the 95/95 value successfully when the figure of merit has one-sided tolerance limit where either the upper or lower limit exits. However, when it is necessary to cut off the tails of 2.5% evenly in both ends, namely the centered two-sided tolerance limit, the suggested formula results in a lower confidence level. Thus, a modified formula is suggested in this study to account for such characteristics, and, as a result, the number of repeated calculations required to obtain the 95/95 value is calculated. The validity of the formula and the number of repeated calculations are examined using numerical experiments for 21 different distributions. The numerical experiment has been conducted with one to ten million sample sets to estimate the confidence level. The results of the numerical experiments indicate that the 95/95 value is predicted successfully by the repeated calculations decided by the modified formula when the figure of merit has characteristics of the centered two-sided distribution, while the existing formula results in a confidence level of 80%.