A Framework for Modeling and Optimizing Maintenance in Systems Considering Epistemic Uncertainty and Degradation Dependence Based on PDMPs

A modeling and optimization framework for the maintenance of systems under epistemic uncertainty is presented in this paper. The component degradation processes, the condition-based preventive maintenance, and the corrective maintenance are described through piecewise-deterministic Markov processes in consideration of degradation dependence among degradation processes. Epistemic uncertainty associated with component degradation processes is treated by considering interval-valued parameters. This leads to the formulation of a multi-objective optimization problem whose objectives are the lower and upper bounds of the expected maintenance cost, and whose decision variables are the periods of inspections and the thresholds for preventive maintenance. A solution method to derive the optimal maintenance policy is proposed by combining finite-volume scheme for calculation, differential evolution, and nondominated sorting differential evolution for optimization. An industrial case study is presented to illustrate the proposed methodology.