A non-parametric dynamic degradation-based inspection and replacement model for single-unit continuously deteriorating systems

This paper deals with a dynamic degradation-based maintenance model for a single-unit continuously deteriorating system without assuming any predefined parametric decision structure or planning scheme. Modeling the system degradation as an inverse Gaussian process with a general shape function, we formulate the condition-based maintenance problem as a semi-Markov decision process (SMDP), where the state consists of both the continuous degradation level and discrete age. Maintenance actions, including the current maintenance activity and the next inter-inspection interval, are dynamically determined at each decision epoch by minimizing the long-run average cost rate. The cost associated with each action accounts not only for the immediate maintenance expense, but also for potential future losses due to system downtime. While most related works discretize the continuous degradation process to facilitate the SMDP resolution, we propose an alternative approach using dynamic programming with function approximation to avoid the loss of Markov property of the state space. Specifically, we apply the data transformation technique to convert the SMDP into an equivalent Markov decision process and then introduce a relative value iteration algorithm with k-nearest neighbors regression to solve the problem. Extensive numerical analyses demonstrate that the proposed dynamic maintenance model effectively adapts to various degradation behaviors and maintenance costs, outperforming conventional models, particularly those relying on periodic inspection schemes or on non-periodic inspections but with degradation discretization.