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Recursive Formulas for the Reliability of MultiState Consecutivekoutofn:F System

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In traditional reliability theory, both the system and its components are allowed to take only two possible states: working or failed. In a multistate system, both the system and the components are allowed to be in M+1 states: 0, 1, 2,…, M, where M is a positive integer which represents a system or unit in perfect functioning state, while zero is complete failure state. A multistate system reliability model provides more flexibility for the modeling of equipment conditions. Huang et al. (2003) proposed more general definitions of the multistate consecutivekoutofn:F and G systems and then provide an exact algorithm for evaluating the system state distribution of decreasing multistate consecutivekoutofn:F systems. Another algorithm is provided to bound the system state distribution of increasing multistate consecutivekoutofn:F and G systems. The multistate consecutivekoutofn:F system is applicable to, for example, quality control problems. In this paper, we provide two theorems and a recursive algorithm which evaluate the system state distribution of a multistate consecutivekoutofn:F system using the theorems. These recursive formulas are useful for any multistate consecutivekoutofn:F system, including the decreasing multistate F system, the increasing multistate F system and other nonmonotonic F systems. We calculate the order of computing time and memory capacity of the proposed algorithm and show that, in cases when the number of components n is large, the proposed algorithm is more efficient than other algorithms. A numerical experiment shows that when n is large, the proposed method is efficient for evaluating the system state distribution of multistate consecutivekoutofn:F systems.

 Date created
 2006

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 Attribution 4.0 International