Multivariate models are essential for evaluating the maintenance of complex degraded industrial systems. Some models of multi-component degradation systems assume that components degrade independently. Although such as assumption allows for tractable mathematical models, it remains unrealistic for systems where stochastic dependence is actually present. Degradation dependent models are usually divided into three groups: multivariate-based methods, copula-based methods, and degradation-rate interaction methods. It is common to find two parts in degrading systems: for example, in heavy machine tools or fatigue cracks in two terminals. The deterioration can be described by a bivariate stochastic process. This work focuses on the study of a system consisting of two dependent components. Their dependence is modelled with the so-called trivariate reduction method as follows: two dependent degradation processes are created from three independent degradation processes. Imperfect preventive maintenance actions are performed periodically every T time units and the overall degradation of the system is reduced in a fixed percentage since its installation. This maintenance model is known as the infinite-order ARD (Arithmetic Reduction of Degradation) model. Furthermore, it is assumed that the system fails when the degradation of a component crosses a predetermined threshold. This failure can only be detected through inspections. Under these assumptions, the first hitting time distribution is developed using a recursive procedure. The analytical cost model is obtained, and the expected cost rate is minimized considering the repair efficiency and the time between preventive maintenance actions as optimization parameters. To illustrate the bivariate model, some numerical examples are given using the Monte-Carlo simulation approach.