Response surface methodology for functional data with application to nuclear safety

The paper proposes an adaptation of Responce Surface Methodology (RSM) when the covariate is a functional data (one or more functions for instance). The key of the method is to combine dimension reduction techniques with usual Design of Experiments. We prove that the good properties of multivariate designs (rotatability, alphabetic optimality,...) are also verified by the functional designs. The good behavior of the method is illustrated on numerical experiments and applied to nuclear safety.