This work aims to investigate the interest in multi-scale uncertainty quantification for nonlinear dynamic systems with friction interfaces. Indeed, such structures experience uncertainties at different time and space scales due to the friction interface. The focus of this work is to quantify and link the uncertainties from friction interfaces at different scales to the nonlinear dynamic response of the structure. A multi-scale kriging approach is employed to propagate the uncertainty. An industrial test rig for dovetail joints will be used as a test case to demonstrate the proposed methodology.