The redundancy allocation problem is to find an optimal allocation of redundant components by considering the set of resources and cost constraints. In this research, the satellite attitude determination and control system is studied and its components is introduced, then the reliability of this system is modeled and optimized based on a mathematical approach based on the redundancy allocation. The model studied in this paper is about the structure of a series-parallel system that is in the exact mode of a satellite attitude determination and control system. In this paper, a new approach for modeling and optimization is presented. The mathematical model presented in this paper is into the class of mixed integer non-linear programming (MINLP). Solving these problems is very important for various researchers due to the high mathematical complexity. In this research, a heuristic method is used to the problem exact solution, the results of which have been reported.