Remaining useful life (RUL) analysis of repairable multi-state components based on Markov process

Multi-state components undergo unidirectional performance degradation over time. Under incomplete maintenance conditions, the repair effectiveness progressively degrades with an increasing number of maintenance interventions. The state transition pathways of components throughout their life-cycle are analyzed using a Markov process. Analytical expressions are derived to calculate the component’s life-cycle duration and the number of maintenance interventions. When the operational history of a component is available, its remaining useful life is predicted from two perspectives: elapsed time and number of maintenance interventions. Moreover, Monte-Carlo methods are employed for both modeling and simulating the problem. The validity of the proposed methodology and analytical expressions is confirmed through case studies by comparing simulation outcomes with analytical solutions.