This paper develops a framework for the extraction of a reliability block diagram in component-based systems for reliability prediction with respect to specific missions. A mission is defined as a composition of several high-level functions occurring at different stages and for a specific time during the mission. The high-level functions are decomposed into lower-level functions, which are then mapped to their corresponding components or component assemblies. The reliability block diagram is obtained using functional decomposition and function-component association. Using the reliability block diagram and the reliability information on the components such as failure rates, the reliability of the system carrying out a mission can be estimated. The reliability block diagram is evaluated by converting it into a logic (Boolean) expression. A modeling language created using the Generic Modeling Environment (GME) platform is used, which enables modeling of a system and captures the functional decomposition and function-component association in the system. This framework also allows for real-time monitoring of the system performance where the reliability of the mission can be computed over time as the mission progresses. The uncertainties in the failure rates and operational time of each high-level function are also considered which are quantified through probability distributions using the Bayesian framework. The dependence between failures of components are also considered and are quantified through a Bayesian network (BN). Other quantities of interest such as mission feasibility and function availability can also be assessed using this framework. Mission feasibility analysis determines if the mission can be accomplished given the current state of components in the system, and function availability provides information whether the function will be available in the future given the current state of the system. The proposed methodology is demonstrated using a radio-controlled (RC) car to carry out a simple surveillance mission.