In traditional reliability theory, both the system and its components are allowed to take only two possible states: working or failed. On the other hand, in a multi-state system, both the system and the components are allowed to be in M+1 states, i.e., 0, 1, 2,…, M. A multi-state system reliability model provides more flexibility for the modeling of equipment conditions. In this paper, we provide a new recursive algorithm for evaluating the system state distributions of generalized multi-state k-out-of-n:F systems. This recursive algorithm is useful for any multi-state k-out-of-n:F system, including the decreasing, increasing and non-monotonic types of multi-state k-out-of-n:F systems. We calculate and compare the orders of computing time and memory capacity of our algorithm with existing algorithms.
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