Maintenance optimisation for systems with multi-dimensional degradation and imperfect inspections

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.