Recursive Formulas for the Reliability of Multi-State Consecutive-k-out-of-n:F System(<Special English Issue>-Information and Operations Management)

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概要

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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 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.

• 社団法人日本経営工学会の論文
• 2006-02-15

著者

• 秋葉 知昭

  山形県立産業技術短期大学校

• Akiba Tomoaki

  Yamagata Coll. Of Ind. & Technol. Yamagata‐shi Jpn

• Akiba T

  Department Of Information Management Engineering Yamagata College Of Industry & Technology

• Akiba Tomoaki

  Information Management Engineering Yamagata College Of Industry And Technology

• Akiba Tomoaki

  Dpt. Of Information Management Engineering Yamagata College Of Industry And Technology

• Akiba Tomoaki

  Information Management Engineering Yamagata College Of Industry & Technology

• Yamamoto Hisashi

  Faculty of System Design, Tokyo Metropolitan University

• NAGATSUKA Hideki

  Faculty of System Design, Tokyo Metropolitan University

• Zuo Ming

  Department of Mechanical Engineering, University of Alberta

• Zuo Ming

  Department Of Mechanical Engineering University Of Alberta

• Nagatsuka Hideki

  Faculty Of System Design Tokyo Metropolitan University

• Yamamoto Hisashi

  Tokyo Metropolitan Univ. Hino‐shi Jpn

• Yamamoto Hisashi

  Faculty Of System Design Tokyo Metropolitan University

• Yamamoto Hisashi

  Department Of System Design Tokyo Metropolitan University

• Yamamoto Hisashi

  Tokyo Metropolitan University

• NAGATSUKA Hideki

  Tokyo Metropolitan University

• 秋葉 知昭

  千葉工業大学

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