In this paper, we define a new methodology to perform sensitivity analysis of a computer simulation code in a particular case, whose study is motivated by a nuclear reliability application. This particular framework is characterized by three features. The first feature is that this kind of code is computationally expensive, which limits the number of available code evaluations. Second, code inputs are scalar and functional parameters, and the functional ones can be dependent. Third, the probability distribution of the functional inputs is not known; only a sample of their realizations is available. The proposed methodology is a combination and an adaption of existing methods. First, the functional input uncertainty is quantified via a functional decomposition combined with a sparse Gaussian mixture model. From this obtained probability density function, a method is proposed to sample uniformly both the functional and scalar input variation domain. Finally, variance-based sensitivity indices are estimated. This methodology is applied to an analytical example to evaluate this approach. Finally, the application to the nuclear reliability study is described.