  Robustness analysis is an emerging field in the domain of uncertainty
quantification. It consists of analysing the response of a computer model with
uncertain inputs to the perturbation of one or several of its input
distributions. Thus, a practical robustness analysis methodology should rely on
a coherent definition of a distribution perturbation. This paper addresses this
issue by exposing a rigorous way of perturbing densities. The proposed
methodology is based the Fisher distance on manifolds of probability
distributions. A numerical method to calculate perturbed densities in practice
is presented. This method comes from Lagrangian mechanics and consists of
solving an ordinary differential equations system. This perturbation definition
is then used to compute quantile-oriented robustness indices. The resulting
Perturbed-Law based sensitivity Indices (PLI) are illustrated on several
numerical models. This methodology is also applied to an industrial study
(simulation of a loss of coolant accident in a nuclear reactor), where several
tens of the model physical parameters are uncertain with limited knowledge
concerning their distributions.
