Designing complex systems for mission-critical applications requires a design process with focus upon maximizing the probability of meeting design requirements. Typically the design process for these systems consists of filtering and refining an initial set of conceptual designs to produce a final set of detailed designs. This final set of designs is presented to the system contracting agency or management team for design selection. In this work, a framework is presented for a multi-stage design process in which the Probability of Correctness (PoC) is utilized as a metric to sequentially filter designs from the abstract conceptual phase through the detailed design phase. This framework utilizes methods for uncertainty propagation (UP) from reliability engineering, which are organized within the framework to match the UP method with the model fidelity and data type available at each stage of the process. A case study using the Advanced Diagnostic and Prognostic Testbed (ADAPT) Electric Power System (EPS) is presented to illustrate both the verification process utilizing multiple UP methods, and also the use of the OpenModelica environment for system design. A discussion presents a generalization of the framework and the future work needed to realize the comprehensive framework for system design.