A systematic method is proposed to approach complete fault coverage for catastrophic faults in analog circuits. In the proposed method, a fault propagation graph is first created from the circuit netlist. Standard graph theory techniques are then employed to identify a minimal set of observation points (MOP) such that, by monitoring these points, complete fault coverage can be achieved, i.e., all potential catastrophic faults of the circuit can be detected theoretically. The developed method is valuable because of the increasingly critical quality requirements for modern IC applications and the lack of existing methods that can achieve sub-ppm test escapes in the state-of-the-art. A widely used benchmark circuit, a CMOS operational amplifier, is utilized to demonstrate and validate the method. Simulation results show that all catastrophic faults can be detected by monitoring the identified MOP.