Random telegraph noise (RTN) is a critical reliability metric impacting the memory state during read operation in resistive switching memory. In this study, we develop a time-efficient (a) slow ramped stress technique for quantitative RTN assessment to determine the disturb voltage (VDIST) for oxygen vacancy perturbations in the filament. The technique is used to (b) identify the best regimes of operation for RRAM with superior RTN robustness and (c) investigate dielectric material properties that govern stability of the filament using the thermochemical bond breaking / ionic migration transport model as the basis. The proposed method is exemplified comparing HfOx and AlOx stacks. Shape and size of filament in high resistance state (HRS) has a big impact on RTN.