This paper proposes a new GO method for repairable systems with multiple unstable operation states. First, multi-state signal flow and multi-state GO operator are defined, respectively. And the formula for calculating state probability of unit with multiple unstable operation states is deduced based on Markov theory. Furthermore, a new function GO operator named Type 19 is created to describe the unit stabilizing property. And its GO operation formulas for reliability analysis are deduced. On this basis, the reliability analysis process of multi-state repairable systems based on the new GO method is formulated. Then, this new GO method is applied in reliability analysis of Hydraulic Oil Supply System of a heavy vehicle. In order to verify the feasibility, advantage and reasonability of the new GO method, its analysis result is compared with those of FTA and the existing GO method for two-state repairable systems. All in all, this paper not only improves the theory of GO method, and widens the application of GO method, but also provides a new approach for reliability analysis of multi-state repairable systems.

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