Second-Order Uncertainty Analysis for Radiation Shielding Problems Using MCNP

Standard uncertainty propagation is based on a first-order Taylor expansion. This approximation is usually justified by assuming that 'uncertainties are very small numbers compared with the values of their corresponding quantities'. Furthermore, the second derivatives needed for a second-order analysis are not usually available, and a second-order analysis requires more knowledge regarding the distribution of the random variables. For radiation shielding problems, the MCNP6 Monte Carlo code computes first and second derivatives of a response with respect to nuclide density or reaction cross section. This paper explores the application of these derivatives to second-order uncertainty analysis