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In this paper, we develop a generalized multi-state degraded system reliability model subject to multiple competing failure processes, including two degradation processes, and random shocks. The operating condition of the multi-state systems is characterized by a finite number of states. We also present a methodology to generate the system states when there are multi-failure processes. The model can be used not only to determine the reliability of the degraded systems in the context of multi-state functions, but also to obtain the states of the systems by calculating the system state probabilities. Several numerical examples are given to illustrate the concepts.