Evaluation of nuclear safety from the outputs of computer codes in the presence of uncertainties

Abstract We apply methods from order statistics to the problem of satisfying regulations that specify individual criteria to be met by each of a number of outputs, k, from a computer code simulating nuclear accidents. The regulations are assumed to apply to an ‘extent’, γk, (such as 95%) of the cumulative probability distribution of each output, k, that is obtained by randomly varying the inputs to the code over their ranges of uncertainty. We use a ‘bracketing’ approach to obtain expressions for the confidence, β, or probability that these desired extents will be covered in N runs of the code. Detailed results are obtained for k=1,2,3, with equal extents, γ, and are shown to depend on the degree of correlation of the outputs. They reduce to the proper expressions in limiting cases. These limiting cases are also analyzed for an arbitrary number of outputs, k. The bracketing methodology is contrasted with the traditional ‘coverage’ approach in which the objective is to obtain a range of outputs that enclose a total fraction, γ, of all possible outputs, without regard to the extent of individual outputs. For the case of two outputs we develop an alternate formulation and show that the confidence, β, depends on the degree of correlation between outputs. The alternate formulation reduces to the single output case when the outputs are so well correlated that the coverage criterion is always met in a single run of the code if either output lies beyond an extent γ, it reduces to Wilks' expression for un-correlated variables when the outputs are independent, and it reduces to Wald's result when the outputs are so negatively correlated that the coverage criterion could never be met by the two outputs of a single run of the code. The predictions of both formulations are validated by comparison with Monte Carlo simulations.