Joint Optimization of Condition-Based Maintenance and Performance Control for Linear Multi-State Consecutively Connected Systems

Industrial systems such as signal relay stations and oil pipeline systems can be modeled as linear multi-state consecutively connected systems, which comprise sequentially ordered elements and fail if the first and the final elements are not connected. The performance level of each element is controllable, which determines how many elements an element can connect and affects its degradation rate. Accumulated degradation can cause element failure, which may lead to costly system failure. This paper aims to minimize long-term maintenance-related costs, including system failure costs. We provide optimal maintenance planning and performance control for every system degradation state through Markov decision process modeling and a dynamic programming algorithm. Load-sharing, restricted maintenance capacity, maintenance setup costs, and the structural characteristics of the system are considered in the model, all of which influence the optimal maintenance and performance control policy. Regarding degradation management, reducing the difference in degradation levels between elements, e.g., replacing more-degraded elements first, can be cost-effective. However, increasing the difference in degradation by maintenance or performance control can also lower maintenance-related costs in specific situations, which is discussed in numerical experiments. We also illustrate structural insights regarding the proposed model, including sensitivity analyses of maintenance capacity, setup costs, and the difference between preventive and corrective replacement costs.