Discussion of paper by Matieyendou Lamboni, Hervé Monod, David Makowski “Multivariate sensitivity analysis to measure global contribution of input factors in dynamic models”, Reliab. Eng. Syst. Saf. 99 (2011) 450-459

In the subject paper, a new set of sensitivity indices for multivariate outputs are defined when the uncertainty on the input factors is either discrete or continuous and when the dynamic model is either discrete or functional. Admittedly, these indices can quantify the contribution of each input factor to each principal component and the total inertia reasonably, and provide rich information on dynamic model behaviour. However, Propositions 2-4 in the subject paper which claim that the generalized sensitivity index is equal to the sensitivity index defined on the sum of the principal components are not correct. These incorrect propositions are concluded by the incorrect derivation in the Appendices B and C of the subject paper. This discussion intends to clarify this issue associated with the paper.