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Improved upper bounds for the reliability of d‐dimensional consecutive‐k‐out‐of‐n : F systems

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  • Anant P. Godbole
  • Laura K. Potter
  • Jessica K. Sklar

Abstract

Consider a 2‐dimensional consecutive‐k‐out‐of‐n : F system, as described by Salvia and Lasher [9], whose components have independent, perhaps identical, failure probabilities. In this paper, we use Janson's exponential inequalities [5]; to derive improved upper bounds on such a system's reliability, and compare our results numerically to previously determined upper bounds. In the case of equal component‐failure probabilities, we determine analytically, given k and n, those component‐failure probabilities for which our bound betters the upper bounds found by Fu and Koutras [4] and Koutras et al. [6]. A different kind of analytic comparison is made with the upper bound of Barbour et al. [3]. We further generalize our upper bound, given identical component‐failure probabilities, to suit d‐dimensional systems for d ≤ 3. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 219–230, 1998

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:45:y:1998:i:2:p:219-230
    DOI: 10.1002/(SICI)1520-6750(199803)45:23.0.CO;2-B
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    References listed on IDEAS

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    1. A. D. Barbour & Ourania Chryssaphinou & Malgorzata Roos, 1996. "Compound poisson approximation in systems reliability," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(2), pages 251-264, March.
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    Cited by:

    1. 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.
    2. Xiao, Hui & Yi, Kunxiang & Liu, Haitao & Kou, Gang, 2021. "Reliability modeling and optimization of a two-dimensional sliding window system," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    3. Yi, He & Balakrishnan, Narayanaswamy & Li, Xiang, 2023. "Reliability of three-dimensional consecutive k-type systems," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    4. Lin, Cong & Zeng, Zhaoyang & Zhou, Yan & Xu, Ming & Ren, Zhanyong, 2019. "A lower bound of reliability calculating method for lattice system with non-homogeneous components," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 36-46.

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