Failure interactions and multiple states are two common phenomena in engineering systems. However, most of the redundancy allocation problems assume binary states and ignore failure interactions, which will cause inaccurate and misleading results. Although some research work focuses on the multistate systems, failure interactions have been ignored. This paper, for the first time, solves the redundancy allocation problems considering the systems having both multiple states and failure interactions. The system studied in this paper is a kind of multistate system containing a main subsystem and an auxiliary subsystem with the failure interaction existing from the auxiliary subsystem to the main subsystem. Semi-Markov process is proposed as the model for the system analysis, and a reliability measure, availability, is obtained based on the proposed semi-Markov process models. The system availability is used as the constraint in the redundancy allocation problem. A case study from a navy application is presented to demonstrate the applicability of the proposed method.

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