Markov modeling method for availability of two-item system under passivation

Aiming at the problem that the assumed spare part demand does not depend on the number of available working systems in Metric model, which leads to underestimated availability, considering the passivation state (where the fault-free parts in the failure system do not generate spare part depend), this paper proposes a Markov modeling method for availability in two-item systems under passivation. Firstly, the system spare part state is described as a three-dimensional array consisting of the number of available working systems, stock and backorder, then according to the continuous time Markov chain (CTMC) method, the influence of the fault repairing process of different parts on the state transition is analyzed, two groups of Markov random processes are constructed. Furthermore, the relationship between these two kinds of random processes is analyzed; after merging these two random processes, a Markov state transition model of the spare parts is built, and the expected backorders (EBO) of the spare parts and the instantaneous and steady-state values of the system availability are solved with the model. Finally, the proposed model was used in numerical examples, and the result shows that the EBO and availability of the two-item system calculated using CTMC method are closer to the simulation results compared with those using Metric model.