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As technology scales, more and more memory cells can be placed in a die. Therefore, the probability that a single event induces multiple bit upsets (MBUs) in adjacent memory cells gets greater. Generally, multibit error correction codes (MECCs) are effective approaches to mitigate MBUs in memories. In order to evaluate the robustness of protected memories, reliability models have been widely studied nowadays. Instead of irradiation experiments, the models can be used to quickly evaluate the reliability of memories in the early design. To build an accurate model, some situations should be considered. Firstly, when MBUs are presented in memories, the errors induced by several events may overlap each other, which is more frequent than single event upset (SEU) case. Furthermore, radiation experiments show that the probability of MBUs strongly depends on angles of the radiation event. However, reliability models which consider the overlap of multiple bit errors and angles of radiation event have not been proposed in the present literature. In this paper, a more accurate model of memories with MECCs is presented. Both the overlap of multiple bit errors and angles of event are considered in the model, which produces a more precise analysis in the calculation of mean time to failure (MTTF) for memory systems under MBUs. In addition, memories with scrubbing and nonscrubbing are analyzed in the proposed model. Finally, we evaluate the reliability of memories under MBUs in Matlab. The simulation results verify the validity of the proposed model.