In this work we will study the thermodynamics properties of the quenched decorated Ising model with competitive interactions through the effective field theory (EFT) of a one-spin cluster. This model is used here to describe the thermodynamics properties of the cooper-based oxide superconductors compounds in its insulating phase (antiferromagnetic). The model consists of planes in which the nodal spins interact antiferromagnetically (JA<0) with their nearest-neighbors and ferromagnetically (JF>0) with the spins that decorated the bonds, which are quenched randomly distributed over the two-dimensional lattice. The planes interact antiferromagnetically with weak exchange interaction (i.e., JA′=λJA, λ=10 -5). By using the framework of an effective-field theory, based on the differential operator technique, we discuss beyond thermodynamics properties the antiferromagnetic-phase stability limit in the temperature-decorated bond concentration space (T×p), for λ=10-5 and various values of frustration parameter (α=JA/JF), magnetic field (H) and concentration parameter (p). For certain range of the parameter α we observe a reentrant behavior in low-temperature that it reflects in the properties behavior itself. © 2013 Elsevier B.V. All rights reserved.