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# Recursive Formulas for the Reliability of Multi-State Consecutive-k-out-of-n:F System Open Access

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Type of item
Journal Article (Published)
Language
English
Place
Time
Description
In traditional reliability theory, both the system and its components are allowed to take only two possible states: working or failed. In a multi-state 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 multi-state system reliability model provides more flexibility for the modeling of equipment conditions. Huang et al. (2003) proposed more general definitions of the multi-state consecutive-k-out-of-n:F and G systems and then provide an exact algorithm for evaluating the system state distribution of decreasing multi-state consecutive-k-out-of-n:F systems. Another algorithm is provided to bound the system state distribution of increasing multi-state consecutive-k-out-of-n:F and G systems. The multi-state consecutive-k-out-of-n: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 multi-state consecutive-k-out-of-n:F system using the theorems. These recursive formulas are useful for any multi-state consecutive-k-out-of-n:F system, including the decreasing multi-state F system, the increasing multi-state F system and other non-monotonic 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 multi-state consecutive-k-out-of-n:F systems.
Date created
2006
DOI
doi:10.7939/R3Z31P25J
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Citation for previous publication
Akiba, T., Nagatsuka, H., Yamamoto, H., and Zuo, M. (2006). Recursive Formulas for the Reliability of Multi-State Consecutive-k-out-of-n:F System. The Journal of Japan Industrial Management Association, 56(6), 439-446.
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