Aiming at the limitations of present multi-state systems in characterizing hierarchical performance requirements, a more general dual hierarchical multi-state weighted k-out-of-n system is defined. A new method combining hierarchical operators with universal generation functions is developed to solve the problem of weight dependencies across the different levels to access the availability of the proposed system. Then, the system total cost optimization model under the availability constraint is constructed to study the problem of integrated selection of subsystems and components in system design. The genetic algorithm is adopted to obtain the economic quantities of various subsystems and components. Finally, a power system is demonstrated for the correctness of the presented approach and the effects of the dual hierarchical performance requirements on system availability and cost. The results can offer implications for the design optimization of complex systems under different performance requirements.