A hypothesis that probability giving Δ(1/Vset) [= 1/Vset(n) - 1/Vset(n+1)] > 0, P[Δ(1/Vset) > 0], increases with increasing the number of filaments contained in one memory cell, Nfila, and decreases with increasing switching cycle, n, was made to validate a multi-filament model (MFM) as a mechanism causing the cycle to cycle dispersion of Vset in ReRAM. Here, Δ(1/Vset) is the difference between the inverse of set voltages after n-th and (n+1)-th reset processes. This in turn means that Vset will decrease with increasing Nfila and will increase with increasing n. In addition, another hypothesis that probability giving Δ(1/R) [= 1/Rn - 1/Rn+1] > 0, P[Δ(1/R) > 0], agrees with P[Δ(1/Vset) > 0] was made by incorporating the assumption that vset depends on d with the MFM. Here, Rn, vset, and d represent resistance in high resistance state after the n-th reset process, the set voltage of each filament, and the thickness of a gap between the electrode and the edge of the filament. The validity of these two hypotheses were confirmed by measuring the dependence of P[Δ(1/Vset) > 0], P[Δ(1/R) > 0], and the mean value of Vset, <Vset>, on both the length of the perimeter, L, and n of Pt/NiO/Pt structures to which filaments were introduced by etching the NiO layer.