The relationship between SET-state current level and read-disturb failure time in a tungsten oxide RRAM is characterized and modeled. Our result shows that read voltage-induced reduction of oxygen vacancy density in tungsten oxide follows a power law dependence on cumulative read-disturb time. The power factor is independent of SET-state current level. Read-disturb failure time is considerably improved by several orders of magnitude as SET-state current level increases a few times. An analytical model to correlate SET-state current level and read-disturb failure time is proposed. Since SET-state current level is related to a cross-section of a conductive filament in an oxide, our model is developed based on a relationship between oxide area and critical oxide trap (oxygen vacancy) density from an oxide breakdown model. The validity of the proposed model is supported by experiment results.