Correlation analysis of degrading systems based on bivariate Wiener processes under imperfect maintenance

This article focuses on the correlation between the degradation levels of the two components that form a system. The degradation evolution of each component is modeled using Wiener processes. Both components are dependent and this dependence is described using the trivariate reduction method. To reduce the degradation and extend the system lifetime, preventive maintenance actions are periodically performed. These preventive maintenance actions are imperfect and they are modeled by using an arithmetic reduction of degradation of infinite order model with a determined maintenance efficiency parameter. The evolution of the maintained system is analysed by assessing the expectation and variance of both degradation processes at successive maintenance times. The novelty of this work is the analysis of the Pearson correlation coefficient between the degradation levels of the two components. Different properties of the monotonicity of the Pearson correlation coefficient between the two degradation paths are obtained by considering equal maintenance efficiency and equal general time scales functions for the two Wiener degradation processes associated to each degrading component.