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The goal of the present PhD research is to establish a methodology of nuclear data uncertainty quantification (NDUQ) for MCNPX, the continuous-energy Monte-Carlo (M-C) code. The high fidelity (continuous-energy treatment and flexible geometry modelling) of MCNPX makes it the choice of routine criticality safety calculations at PSI/LRS, but also raises challenges for NDUQ by conventional sensitivity/uncertainty (S/U) methods. The methodology developed during this PhD research is fundamentally different from the conventional S/U approach: nuclear data are treated as random variables and sampled in accordance to presumed probability distributions. When sampled nuclear data are used in repeated model calculations, the output variance is attributed to the collective uncertainties of nuclear data. The NUSS (Nuclear data Uncertainty Stochastic Sampling) tool based on this sampling approach, is implemented to work with MCNPX's ACE format of nuclear data, which also gives NUSS compatibility with MCNP and SERPENT M-C codes. In contrast, multigroup uncertainties are used for the sampling of ACE-formatted pointwise-energy nuclear data in a groupwise manner due to the more limited quantity and quality of nuclear data uncertainties. Conveniently, the usage of multigroup nuclear data uncertainties allows consistent comparison between NUSS and other methods (both S/U and sampling-based) that employ the same nuclear data uncertainty format. The first stage of NUSS development focuses on applying simple random sampling algorithm for uncertainty quantification. The effect of combining multigroup and ACE format on the propagated nuclear data uncertainties is assessed. It is found that the number of energy groups has minor impact on the precision of the multiplication factor (k-eff) uncertainty as long as the group structure reflects the neutron flux spectrum. Successful verification of the NUSS tool for propagating nuclear data uncertainties through MCNPX and quantifying MCNPX output parameter uncertainties is obtained. The second stage of NUSS development is motivated by the need for an efficient sensitivity analysis methodology based on global sampling and coupled with MCNPX. For complex systems, the computing time for obtaining a breakdown of the total uncertainty contribution by individual inputs becomes prohibitive when many MCNPX runs are required. The capability of determining simultaneously the total uncertainty and individual nuclear data uncertainty contributions is thus researched and implemented into the NUSS-RF tool. It is based on the Random Balance Design algorithm and is validated by three mathematical test cases for both linear and nonlinear models and correlated inputs. NUSS-RF is then applied to demonstrate the efficient decomposition of total uncertainty by individual nuclear data. However an attempt to decompose total uncertainty into individual contributions using the conventional S/U method shows different decomposition results when the inputs are correlated. The investigation and findings of this PhD work are valuable because of the introduction of global sensitivity analysis into the existing repertoire of nuclear data uncertainty quantification methods. The NUSS tool is expected to be useful for expanding the types of MCNPX-related applications, such as an upgrade to the current PSI criticality safety assessment methodology for Swiss application, for which nuclear data uncertainty contributions can be quantified.