Analytical redundancy relations (ARRs) are used frequently in the arena of diagnosis as well as optimizing, analyzing, and validating of sensors of the system, but less attention has been paid to the development of systematic and efficient approaches for the generation of complete ARRs set. An efficient method for generating the ARRs is presented in this paper and the hypothetical signature matrix (HSM) is obtained consequently. Then the optimal sensor placement problem is mapped onto a special case of the 0-1 integer programming (IP) problem,which is solved by the algorithm of binary particle swarm optimization (BPSO) in the end. The effectiveness of the method is verified by the application of a synthetic example.