Measuring inputs-outputs association for time-depending hazard models under safety objectives using kernels

A methodology for assessing the inputs-outputs association for time-depending predictive models under failure mode for instance is investigated. Firstly, new dependency models for sampling random values of uncertain inputs that comply with the safety objectives are provided. Secondly, the asymmetric role of outputs and inputs leads to develop new kernel-based statistical tests of independence between the inputs and outputs using the dependency models. The associated test statistics are normalized so as to introduce new kernel-based sensitivity indices (Kb-SIs). Such first-order and total Kb-SIs allow for i) assessing the inputs effects on the whole dynamic outputs subjected to safety objectives, ii) dealing with sensitivity functionals (SFs) having heavy-tailed distributions or non-stationary time-depending SFs thanks to kernel methods. Our approach is also well-suited for dynamic models with prescribed copulas of inputs.