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m -Consecutive- k -out-of- n : F Structures with a Single Change Point

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  • Ioannis S. Triantafyllou

    (Department of Computer Science & Biomedical Informatics, University of Thessaly, 35131 Lamia, Greece)

Abstract

In the present article, we introduce the m -consecutive- k -out-of- n: F structures with a single change point. The aforementioned system consists of n independent components, of which the first n 1 units are identically distributed with common reliability p 1 , while the remaining ones share a different functioning probability p 2 . The general setup of the proposed reliability structures is presented in detail, while an explicit expression for determining the number of its path sets of a given size is derived. Additionally, closed formulae for the reliability function and mean time to failure of the aforementioned models are also provided. For illustration purposes, several numerical results and comparisons are presented in order to shed light on the performance of the proposed structure.

Suggested Citation

  • Ioannis S. Triantafyllou, 2020. "m -Consecutive- k -out-of- n : F Structures with a Single Change Point," Mathematics, MDPI, vol. 8(12), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2203-:d:460167
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    References listed on IDEAS

    as
    1. Arapis, Anastasios N. & Makri, Frosso S. & Psillakis, Zaharias M., 2016. "On the length and the position of the minimum sequence containing all runs of ones in a Markovian binary sequence," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 45-54.
    2. Serkan Eryilmaz & Markos V. Koutras & Ioannis S. Triantafyllou, 2011. "Signature based analysis of m‐Consecutive‐k‐out‐of‐n: F systems with exchangeable components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(4), pages 344-354, June.
    3. Dafnis, Spiros D. & Makri, Frosso S. & Philippou, Andreas N., 2019. "The reliability of a generalized consecutive system," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 186-193.
    4. Eryilmaz, Serkan, 2020. "Age-based preventive maintenance for coherent systems with applications to consecutive-k-out-of-n and related systems," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    5. Cui, Lirong & Kuo, Way & Li, Jinlin & Xie, Min, 2006. "On the dual reliability systems of (n,f,k) and," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1081-1088, June.
    6. Chang, Gerard J. & Cui, Lirong & Hwang, Frank K., 1999. "Reliabilities for (n,f,k) systems," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 237-242, July.
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    Cited by:

    1. Li, Mingjia & Hu, Linmin & Wu, Shaomin & Zhao, Bing & Wang, Yan, 2023. "Reliability assessment for consecutive-k-out-of-n: F retrial systems under Poisson shocks," Applied Mathematics and Computation, Elsevier, vol. 448(C).

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