This paper deals with compatible component selection problems, where the goal is to find combinations of components satisfying design constraints given a product structure, component alternatives available in design catalogue for each subsystem of the product, and a preliminary design constraint. An extended Constraint Satisfaction Problem (CSP) is introduced to solve component selection problems considering uncertainty in the values of design variables. To handle a large number of all possible combinations of components, the paper proposes a systematic filtering procedure and an efficient method to estimate a complex feasible design space to facilitate selection of component combinations having more feasible solutions. The proposed approach is illustrated and demonstrated with a robotic vacuum cleaner design example.