In this work, a novel analytical framework is proposed for the risk-based design of complex engineering systems. The risk based-design process is the reverse process of risk propagation that entails the optimum allocation of the desired risk of failure of the system to all of its components. This paper studies the challenges in the design process of complex systems, the mathematical modeling of their topological architecture, and their unique behaviors. These characteristics make it impossible for the designer to use the common reliability and risk methodologies in the design process. The fundamental development of this work is an analytical upper bound for the distribution of risk of failure in the subsystem or element level. This upper bound satisfies the subadditivity condition of a coherent measure of risk. Additionally, its simplicity and low computational cost provide an appropriate framework as a fundamental building block for the risk-based design of complex systems. The proposed methodology is applied to three examples with insignificant desired probability of failure and its accuracy is compared with the Monte Carlo simulation, demonstrating its effectiveness and value.