In the framework of risk assessment in nuclear accidents, simulation tools are widely used to understand and model physical phenomena. These simulation tools take into account a large number of uncertain input parameters. We often use Monte Carlo–type methods to explore their range of variation: The input space is randomly sampled, and a code run is performed on each sampled point. However, some of these code runs may fail to converge. Analyzing these code failures to understand which of the inputs have the most influence on them leads to a better understanding of how the code works. It also intends to improve the robustness of the simulation software and code computations. For this purpose, we propose two complementary approaches performing a statistical analysis of the code failures. The first approach is based on goodness-of-fit tests and compares conditional probability distributions according to code failures to a reference one. A second approach, based on a dependence measure named the Hilbert-Schmidt Independence Criterion, provides another way to measure the global dependence between the inputs and the code failures. The development of this methodology is carried out in the context of severe nuclear accidents. More especially, the presented methods are applied for the study of the simulation code MC3D, which simulates the fuel-coolant interaction in a severe nuclear accident context.