In this article, a method is proposed to conduct a global sensitivity analysis of epistemic uncertainty on both system input and system structure, which is very common in early stage of system development, using Dempster-Shafer theory (DST). In system reliability assessment, the input corresponds to component reliability and system structure is given by system reliability function, cut sets, or truth table. A method to propagate real-number mass function through set-valued mappings is introduced and applied on system reliability calculation. Secondly, we propose a method to model uncertain system with multiple possible structures and how to obtain the mass function of system level reliability. Finally, we propose an indicator for global sensibility analysis. Our method is illustrated, and its efficacy is proved by numerical application on two case studies.