A quite simple diluted Ising-like model has been proposed to describe the order-disorder transformation in the YBa₂Cu₃O_6+x systems. On the basis of the exact solutions are obtained for the short-range and long-range order in the stoichiometric case and for the percolation threshold x_c below which the ordered phase does not appear. The temperature dependence of the long-range order is in good agreement with the experimental results. From the analysis of the percolation threshold the absence of an ordered phase and superconductivity in the composition range of x<0.5 is easily understood.