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Evaluating methods for the reliability of a large 2‐dimensional rectangular k‐within‐consecutive‐(r, s)‐out‐of‐(m, n):F system

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  • Hisashi Yamamoto
  • Tomoaki Akiba

Abstract

A 2‐dimensional rectangular k‐within‐consecutive‐(r, s)‐out‐of‐(m, n):F system consists of m × n components, and fails if and only if k or more components fail in an r × s submatrix. This system can be treated as a reliability model for TFT liquid crystal displays, wireless communication networks, etc. Although an effective method has been developed for evaluating the exact system reliability of small or medium‐sized systems, that method needs extremely high computing time and memory capacity when applied to larger systems. Therefore, developing upper and lower bounds and accurate approximations for system reliability is useful for large systems. In this paper, first, we propose new upper and lower bounds for the reliability of a 2‐dimensional rectangular k‐within‐consecutive‐(r, s)‐out‐of‐(m, n):F system. Secondly, we propose two limit theorems for that system. With these theorems we can obtain accurate approximations for system reliabilities when the system is large and component reliabilities are close to one. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005

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  • Hisashi Yamamoto & Tomoaki Akiba, 2005. "Evaluating methods for the reliability of a large 2‐dimensional rectangular k‐within‐consecutive‐(r, s)‐out‐of‐(m, n):F system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(3), pages 243-252, April.
    • Handle: RePEc:wly:navres:v:52:y:2005:i:3:p:243-252
    DOI: 10.1002/nav.20067
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    References listed on IDEAS

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    1. James Fu & Markos Koutras, 1994. "Poisson approximations for 2-dimensional patterns," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 179-192, March.
    2. Michael V. Boutsikas & Markos V. Koutras, 2000. "Reliability Approximation for Markov Chain Imbeddable Systems," Methodology and Computing in Applied Probability, Springer, vol. 2(4), pages 393-411, December.
    3. Anant P. Godbole & Laura K. Potter & Jessica K. Sklar, 1998. "Improved upper bounds for the reliability of d‐dimensional consecutive‐k‐out‐of‐n : F systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(2), pages 219-230, March.
    4. Tomoaki Akiba & Hisashi Yamamoto, 2001. "Reliability of a 2‐dimensional k‐within‐consecutive‐r × s‐out‐of‐m × n:F system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(7), pages 625-637, October.
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    Cited by:

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    2. Yi, He & Balakrishnan, Narayanaswamy & Li, Xiang, 2023. "Reliability of three-dimensional consecutive k-type systems," Reliability Engineering and System Safety, Elsevier, vol. 233(C).

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