Abstract: The structure reliability or performance assessment of complex systems with both epistemic and aleatory uncertainties is a challenge problem for engineering systems. In this paper, an implementation framework of systems reliability assessment based on the quantification of margins and uncertainties (QMU) methodology is proposed. The description of QMU concept is introduced first, then the Dempster-Shafer Theory of Evidence is used to present the presence of aleatory and epistemic uncertainties in the proposed QMU implementation framework. To alleviate the computational costs, the Kriging model has been implemented as the surrogate for the structure response. Then the structure reliability was presented by a QMU metric in terms of confidence factor(CF). The technique is demonstrated by a numerical example to account for the computational efficiency. The difference between QMU metric and non-probabilistic reliability methods is discussed