Joint optimization of condition-based maintenance and inventory control for a k-out-of-n:F system of multi-state degrading components

•Optimized a condition-based maintenance and spare inventory policy.•Considered stochastic-degrading and multi-state components and k-out-of-n systems.•Used a Markov decision process in combination with dynamic programming algorithm.•Proposed an approach based on the number of components in each degradation state.•Analyzed complexity of the optimization algorithm and evaluated it numerically.