In this paper, we investigate exchange-biased square nanodots whose lateral sizes range between 130 and 500 nm, in comparison with continuous films by kinetic Monte Carlo simulations. We use a granular model which takes into account disordered interfacial phases by considering less stable magnetic grains at the interface in the antiferromagnetic (AF) layer. We further model the effect of the nanofabrication process by considering grains with reduced surfaces at the edges, due to grain cutting. Since less stable grains at the nanodot edges in the AF layer have been experimentally evidenced, we assumed a weaker anisotropy for the grains which are in the AF layer at the dot edges. Our results evidence two different mechanisms of the ferromagnetic (F) layer reversal depending on the magnitude of the coupling between F grains. In the weak coupling regime relative to the anisotropy, the exchange field is independent of the coupling and no variability from one nanodot to another is observed. By contrast, in the strong coupling regime, the exchange field depends on the coupling and it shows a high variability from one nanodot to another. Our model also well explain some experimental features observed in NiFe/IrMn nanodots (for various lateral sizes) and continuous films, at various measurement temperatures and various AF thicknesses. Finally, our model explains a long lasting issue about why the exchange field in nanodots can be either smaller or larger than in continuous films.