Abstract: A system consists of two entangled qubits, where each qubit interacts locally with an environment described by a bosonic bath. The time evolution of the proposed system is obtained analytically by solving its Markovian master equation. The quantum Fisher information is used as an estimator of the phase damping of the initial state settings and the interaction damping parameter. It is exhibited that the initial state settings play a role as a controller of the precision of the estimation degree of these parameters. We classified the state that could be used to estimate the phase damping with high accuracy. Moreover, the constant behavior of the variances of the estimated parameters shows that the optimal estimation could be achieved for small values of the damping parameter. We have discussed the possibility that the amount of quantum Fisher information can be advised as an indicator of the presence of non-classical correlation between the subsystems of the entangled qubit.