A 6-component circular multi-state Markov repairable system with spatial dependence

A Multi-State repairable system with interacting components is built in this paper. The components of the system are arranged in a circle. The performance of each component depends on its four spatial "neighbors". Markov process is adopted to model the performance of the system. Availability of the system is obtained via Markov process theory and Laplace transform method. A numerical example is given to illustrate the results in the paper.