Due to their high density, modern DRAMs are very susceptible to the interactions between adjacent cells, which in turn increases the difficulty and complexity of memory testing. In this work, we studied the interaction mechanisms among neighbouring DRAM cells in order to provide an efficient testing solution. According to the open literature, there are two mechanisms responsible for this interaction: leakage currents and cell state transitions. The frequently used Coupling Fault (CF) model is inadequate to model the combined effect of these mechanisms, while testing procedures using the Neighborhood Pattern Sensitive Fault (NPSF) model are not time efficient solutions. Towards this direction, we propose a new fault model, the Neighborhood Leakage and Transition Fault (NLTF) model for DRAMs, which effectively models the faulty behavior related to neighbouring cell interference. In addition, we developed a new test algorithm which is based on the NLTF model, and provides test application time reductions ranging from 68 to 87 percent with respect to the existing testing algorithms in the literature that are capable to cover the NLTFs. Finally, the proposed algorithm is extended to cover NLTFs in word-oriented DRAMs.