Generalized Tolerance Limit Evaluation Method to Determine Statistically Meaningful Minimum Code Simulations

The tolerance limit approach has been internationally adopted for nuclear safety analyses as a way of identifying more realistic safety limits in the Best Estimate Plus Uncertainty (BEPU) methodology. The approach is based on the Wilks’ formula set suggested by the GRS (Gesellschaft fur Anlagen-und Reaktorsicherheit), and consists of two approaches; one-sided approach to obtain a statistical meaning of the maximum output value in the multiple code runs, and two-sided approach for the minimum and maximum values at the same time. The Wilks’ formula set suggested by the GRS has been employed without questioning any ambiguities in its true meaning, especially in the two-sided approach. In this paper, the formula set is derived based on the binomial distribution as a direct vehicle to the formulas for clarification purposes. This approach is distinguished from the present integral form of the original Wilks’ formula in that it is based on the probability density function and the joint probability density function associated with the order statistics. The purposes of this paper are to derive the true meanings of the present Wilks’ formulas, which are applied in the nuclear safety analysis, and to derive a new set of formulas to determine statistically meaningful minimum number of code runs in the BEPU. An improved formula set, which consists of the Generalized Maximum Tolerance Limit (GMTL) and the Generalized Max-Mini Tolerance Limit (GMMTL), is proposed with an emphasis on a new form of the two-sided formula: Centered Two-sided Tolerance Limit (CTTL) formula, which is directly derived from the GMMTL formula. For example, a minimum number of 146 code runs is suggested in lieu of the present 93 code runs to achieve the 95th percentile with 95% confidence in the two-sided approach.© 2008 ASME