Building resilience into today's complex infrastructures is critical to the daily functioning of society and its ability to withstand and recover from natural disasters, epidemics, and cyber-threats. This study proposes quantitative measures that capture and implement the definition of engineering resilience advanced by the National Academy of Sciences. The approach is applicable across physical, information, and social domains. It evaluates the critical functionality, defined as a performance function of time set by the stakeholders. Critical functionality is a source of valuable information, such as the integrated system resilience over a time interval, and its robustness. The paper demonstrates the formulation on two classes of models: 1) multi-level directed acyclic graphs, and 2) interdependent coupled networks. For both models synthetic case studies are used to explore trends. For the first class, the approach is also applied to the Linux operating system. Results indicate that desired resilience and robustness levels are achievable by trading off different design parameters, such as redundancy, node recovery time, and backup supply available. The nonlinear relationship between network parameters and resilience levels confirms the utility of the proposed approach, which is of benefit to analysts and designers of complex systems and networks.