In this paper, we develop a maintenance model for systems subjected to multiple correlated degradation processes, where a multivariate stochastic process is used to model the degradation processes, and the covariance matrix is employed to describe the interactions among the processes. The system is considered failed when any of its degradation features hits the pre-specified threshold. Due to the dormancy of degradation-based failures, inspection is implemented to detect the hidden failures. The failed systems are replaced upon inspection. We assume an imperfect inspection, in such a way that a failure can only be detected with a specific probability. Based on the degradation processes, system reliability is evaluated to serve as the foundation, followed by a maintenance model to reduce the economic losses. We provide theoretical boundaries of the cost-optimal inspection intervals, which are then integrated into the optimisation algorithm to relieve the computational burden. Finally, a fatigue crack propagation process is employed as an example to illustrate the effectiveness and robustness of the developed maintenance policy. Numerical results imply that the inspection inaccuracy contributes significantly to the operating cost and it is suggested that more effort should be paid to improve the inspection accuracy.

在本文中，我们为遭受多个相关退化过程的系统开发了一个维护模型，其中使用多元随机过程对退化过程进行建模，并采用协方差矩阵来描述过程之间的相互作用。当系统的任何退化特征达到预先指定的阈值时，系统被视为失败。由于基于退化的故障的休眠，实施检查以检测隐藏的故障。故障系统在检查后更换。我们假设不完美的检查，这样一个故障只能以特定的概率被检测到。以退化过程为基础，对系统可靠性进行评估，然后建立维护模型，以减少经济损失。我们提供了成本最优检查间隔的理论边界，然后将其集成到优化算法中以减轻计算负担。最后，以疲劳裂纹扩展过程为例来说明所开发维护策略的有效性和稳健性。数值结果表明检查不准确度对运营成本有显着影响，建议应该付出更多努力来提高检查准确度。