The continuous pursuits of developing a better, safer, and more sustainable system have pushed systems to grow in complexity. As complexity increases, challenges consequently arise for system designers in the early design stage to take account of all potential failure modes in order to avoid future catastrophic failures. This paper presents a resilience allocation framework for resilience analysis in the early design stage of complex engineering systems. Resilience engineering is a proactive engineering discipline that focuses on ensuring the performance success of a system by adapting to changes and recovering from failures under uncertain operating environments. Utilizing the Bayesian network (BN) approach, the resilience of a system could be analyzed and measured quantitatively in a probabilistic manner. In order to ensure that the resilience of a complex system satisfies the target resilience level, it is essential to identify critical components that play a key role in shaping the top-level system resilience. Through proper allocation of resilience attributes to these critical components, not only target could resilience requirements be fulfilled, global cascading catastrophic failure effects could also be minimized. An electrical distribution system case study was used to demonstrate the developed approach, which can also be used as a fundamental methodology to quantitatively evaluate resilience of engineered complex systems.