A two-unit system subject to imperfect maintenance is analyzed in this chapter. The deterioration of the system follows a bivariate Wiener degradation process. This process is built from the trivariate reduction method by sharing a common noise that describes the dependence between both units. This dependence is measured through the Pearson's correlation coefficient between both degradation trajectories of the bivariate Wiener process at time t. A maintenance strategy consisting of periodic inspections in which the accumulated deterioration of the system is reduced by a certain quantity is implemented. Some results on the monotonicity of the Pearson's correlation coefficient in different scenarios are obtained.