First hitting time distribution and cost assessment in a two-unit system with dependent degradation processes subject to imperfect maintenance

This paper proposes a degradation model for a two-unit series system, where the components exhibit dependence and are subject to imperfect maintenance. The interdependence between both components is captured using the trivariate reduction method. The system failure occurs when the degradation level of either component exceeds a predetermined threshold. The main motivation of this work is to develop a preventive maintenance strategy for this system, incorporating periodic imperfect maintenance actions in order to extend its useful lifetime. These actions aim to reduce the accumulated degradation level of each component from its installation in a fixed percentage, following the Arithmetic Reduction of Degradation model of infinite order. Another goal is to derive the distribution of time to the system failure, which provides crucial insights into the system's reliability and performance, especially in the case of bivariate degradation. Additionally, a cost model for this maintenance strategy is developed and several numerical examples are presented to illustrate the practical implications. The maintenance decision variables are optimized in order to obtain the minimal expected cost rate within a finite time horizon.