Reply to “Comments on ‘Evaluation of nuclear safety from the outputs of computer codes in the presence of uncertainties’ by W.T. Nutt and G.B. Wallis,” by Y. Orechwa

We respond to comments regarding a previous paper. We conclude that both the coverage and bracketing approaches to statistical sampling are valid and self-consistent. They differ in the underlying probabilistic statement of the criteria. A re-examination of the application of multiple criteria to decision making in nuclear safety leads us to an alternative approach we have called the testing approach. In this approach the physical criteria may be absorbed into a "black box" in which the code makes calculations and the whole process is treated as a test of a single outcome in non-parametric statistics. Using the testing approach one can determine whether or not computer code outputs simultaneously satisfy a set of physical criteria with 95% confidence that the criteria are satisfied with 95% probability, using only 59 runs. This conclusion is independent of the number of criteria and of any inter-dependencies between the outputs from the code.