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Resistive-switching memory (RRAM) devices are attracting a considerable interest in view of their back-end integration, fast programming, and high scalability. Prediction of the programming voltages and currents as a function of the operating conditions is an essential task for developing compact and numerical models able to handle a large number (106 - 109) of cells within an array. Based on recent experimental findings on the set and reset processes, we have developed physics-based analytical models for the set and reset operations in NiO-based RRAMs. Simulation results obtained by the analytical models were compared with experimental data for variable pulse conditions and were found consistent with data. The set transition is described by a threshold switching process at the broken conductive filament (CF), while the reset transition is viewed as a thermally driven dissolution and/or oxidation of the CF. Set and reset models are finally used for reliability predictions of failure times under constant-voltage stress (read disturb) and elevated-temperature bake (data retention).