Stochastic media is important in many fields of nuclear engineering including reactor design, radiation transport applications, and reactor safety. This project will assess the impact of the random fragmentation of fuel assemblies on reactivity and kinetic parameters, including the multiplication factor, the effective delayed neutron fraction, and the effective neutron generation time. Fuel assemblies with UOX and MOX configurations will be evaluated. Two randomization methods have been proposed for numerical analysis of eigenvalue problems: quenched disorder and annealed disorder models. Further exercises include analyzing the impact of the choice of the free parameter of the randomization method and computing the quantity of the moderator after a severe accident scenario that would lead to fuel degradation and have an impact on the re-criticality risk. The methodology proposed in this work can be applied to the evaluation of criticality safety to prevent future accidents.