An optimal multi-level inspection and maintenance policy for a multi-component system with a protection component

Abstract

Protection components are commonly seen in systems with failure propagations. When the protection components are also subject to failures, inspection and maintenance (IM) for main components (i.e., components that directly contribute to the system's performance) and protection components must be designed separately. This task is challenging when the failure propagation only occurs on some failure modes of the components, which remains underexplored by far. In this paper, we design an optimal IM policy for such a system. First, we propose a novel IM policy that outperforms some existing IM policies, including both system-level and component-level IM schemes. Based on the proposed policy, we model the system's state transition behaviors based on the Markov regenerative process (MRGP) and analytically obtain its steady-state behavior. The system's long-term profit rate is quantitatively modeled. Next, the IM policy optimization problem is decomposed, where the master problem involves only discrete variables, while the subproblem contains a single continuous variable. A tailor-made Simulated Annealing-Adaptive Moment Estimation (SA-ADAM) algorithm is developed, in which the SA algorithm solves the master problem, while the ADAM algorithm is employed to solve the subproblem in each iteration of the SA algorithm. The required information for the ADAM algorithm, such as the partial derivative of the long-term profit rate with respect to the inspection interval of the protection component, is derived analytically. A case study of a community power distribution system is presented to demonstrate the superiority of both the proposed multi-level IM policy and the developed SA-ADAM algorithm.