Industrial systems normally present interrelated parts that influence the system performance. For instance, lighting systems composed of many LED lamps, which present a likely dependence because of their common usage. Maintenance actions are performed on these systems to mitigate the degradation effects and widen their lifetime. In this work, imperfect maintenance actions are implemented by using the so-called ARD (Arithmetic Reduction of Degradation) model. With it, the reduction is performed in the overall degradation accumulated in the system since the beginning.

In this framework, the inference problem in a two-component degrading system is analysed. The system degradation follows a bivariate Wiener process, whose dependence is modelled using the trivariate reduction method. Maximum likelihood method is employed for parameter estimation. When parameters are estimated from a degradation model, they usually are estimated from degradation observations, or for failure observations. The novelty of this work is that model parameters are estimated from maintenance information. It is assumed that maintenance data are collected in an unbalanced design, which means that the data from both degradation processes are not necessarily measured at the same time.  Different observation strategies are considered, so that degradation levels can be observed between maintenance actions, as well as just before or just after maintenance times.