The authors present a new numerical analysis method to investigate the conduction filament dynamics of a resistive switching nonvolatile metal-insulator-metal structured memory device. This comprehensive method, utilizing the Gibbs free energy criteria as a leading indicator and allowing simulation of all resistive memory operational phases (forming, set and reset), is presented for the first time. The formation and rupture of an oxygen vacancies based conduction filament are simulated to demonstrate a cycle of operation in a hafnium oxide based resistive forming layer. Starting from a random initial distribution of defect states, on to a formed conduction filament and ending in a ruptured state. Detailed plots of the physical parameters within the resistive layer are provided to gain deeper understanding of the conduction filament kinetics and introduce the concept of "hot spots", referring to random localized initial agglomeration of oxygen vacancies in which temperature surges is favored and contribute to initiate the conductive filament formation. By basing the method on well known thermodynamic properties and the Metropolis algorithm, simulation reliability and efficiency are obtained. The presented results confirm previously published data demonstrating the switching characteristics of hafnium based resistive random access memory.