In this work, we proposed a methodology for robust designs of brake systems in regard to stability and squeal noise. The presented approach consists of two main steps namely the global sensitivity analysis and the Kriging modeling. The first step allows ordering mechanical parameters with respect to their influences on the stability behavior. This is carried out by determining Sobol indices. As a result, parameters having high Sobol indices and which are known to admit dispersions are taken into account to ensure robustness of the stability analysis while non influential parameters are fixed to their nominal values. The second step is related to the use of the Kriging formalism to built a surrogate model to represent accurately and efficiently the stability behavior of the brake system. This tool is shown to be an interesting alternative to finite element models since it has permitted to predict robust stability properties by solving a smaller number of CEA problems. In future works, the possibility of using Kriging models for the estimation of vibration levels of self-excited frictional systems should be carried out.