Managing component degradation in series systems for balancing degradation through reallocation and maintenance

In a physical system, components are usually installed in fixed positions that are known as operating slots. Due to such reasons as user behavior and imbalanced workload, a component’s degradation can be affected by the corresponding installation position in the system. As a result, components degradation levels can be significantly different even when the components come from a homogeneous population. Dynamic reallocation of the components among the installation positions is a feasible way to balance the extent of the degradation, and hence, extend the time from system installation to its replacement. In this study, we quantify the benefit of incorporating reallocation into the condition-based maintenance framework for series systems. The degradation of components in the system is modeled as a multivariate Wiener process, where the correlation between the degradation is considered. Under the periodic inspection framework, the optimal control limits for reallocation and preventive replacement are investigated. We first propose a reallocation policy of two-component systems, where the degradation process with reallocation and replacement is formulated as a semi-regenerative process. Then the long-run average operational cost is computed based on the stationary distribution of its embedded Markov chain. We then generalize the model to general series systems and use Monte Carlo simulations to approximate the maintenance cost. The optimal thresholds for reallocation and replacement are obtained from a stochastic response surface method using a stochastic kriging model. We further generalize the model to the scenario of an unknown degradation rate associated with each slot. The proposed model is applied to the tire system of a car and the battery system of hybrid-electric vehicles, where we show that the reallocation policy is capable of significantly reducing the system’s long-run average operational cost.