The effect of switching layer thickness on achieving tri-mode switching in HfOx-based resistive random access memory (RRAM) has not been explored. Here, we systematically investigate Pt/HfOx/Ti RRAM with different HfOxthicknesses (5, 10, and 15 nm) and reveal that the device with 10 nm HfOxthicknesses can achieve tri-mode switching. Compared with devices with 5 and 15 nm HfOxthicknesses, the digital switching mode of the device with 10-nm HfOxthickness is controlled by the formed conductive filaments (CFs) and the HfOx/Ti interface. The interface-dominated analog switching mode is achieved by modulating the oxygen vacancy concentration at the HfOx/Ti interface under low bias voltage. The occurrence of the write-once-read-many switching mode is due to the continuous accumulation of Joule heating without compliance current (CC), resulting in the formation of an irreversible conductive channel. This work provides a concise and mechanism-clear route for integrating storage, computing, and security functions in reconfigurable in-memory computing applications.