The advantages of the multiple observation time approach for fault diagnosis have been demonstrated before by a fault diagnosis procedure based on partial specification of initial states. It was also shown that it is possible to perform fault simulation under the multiple observation time approach at very low computational overhead compared to conventional simulation. In this work, we combine these procedures and propose a low-complexity fault diagnosis procedure under the multiple observation time approach. Several observations made in this work allow us to increase the effectiveness of the proposed diagnosis scheme in terms of the resolution it achieves and its complexity.