Constant voltage Time-Dependent Forming (TDF) measurements in as-deposited Pt/NiO/Pt stack structures have been conducted. From TDF characteristics, formation of conductive filaments at forming process by applying voltage follows weakest link theory. Furthermore, weakest spots are almost randomly distributed in NiO thin films according to Poisson statistics, each of which can contribute conductive paths locally generated. A “percolating layer” in which the conductive filaments percolate by applying voltage may exist in the NiO thin film. The thickness of the layer is much smaller than that of NiO thin films.