© 2017 Elsevier B.V. The impact of the voltage ramp rate (RR) on the set and reset transition voltages of resistive RAM (ReRAM) devices that form part of one transistor-one resistor (1T1R) structures is investigated. Similar expressions for the set and reset voltages as a function of RR are found, which indicates a common physical origin. Constant voltage stress experiments were also carried out in order to obtain further insight into the acceleration law behind the formation and dissolution of the filamentary path spanning the oxide film. The obtained results seem to be consistent with the thermochemical model (E-model) of dielectric breakdown. The connection between the modification of the set/reset voltages with RR and the shifts of the memory map of the device (the so-called hysteron loop) is also discussed.