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. Hereto, an efficient method named successive elimination is presented. Based on the primary relations (PRs) of system, this method generates complete ARRs set as well as consequent hypothetical signature matrix (HSM) by several elimination loops. On the strength of HSM, the optimal sensor placement problem is mapped onto a special case of the 0-1 integer programming (IP) problem, which is solved by an algorithm of branch-and-bound in the end. Application results show that this method can decrease sensor number and testing cost without decreasing FDR and FIR and it’s beneficial to the sensor placement problem for fault diagnosis.