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On the importance measures of Markov chain imbeddable reliability systems: some advances for k-out-of-n: G and consecutive-k-out-of-n: G structures

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  • Ioannis S. Triantafyllou

    (University of Piraeus
    Graphic Era Deemed to Be University)

Abstract

In the present paper, we study the Birnbaum’s Reliability Importance measures of the components for Markov Chain Imbeddable structures. A generating function approach is presented for determining the Birnbaum’s importance measure for a reliability system consisting of independent and identically distributed components. The general setup is implemented for two specific members of the class of Markov Chain Imbeddable structures. The resulting recurrences for computing the corresponding important measures are established. More precisely, the consecutive-k-out-of-n: G system and the k-out-of-n: G system are under investigation. For the first-mentioned structure a recursive scheme (accompanied with the necessary set of initial conditions) for the Birnbaum’s importance measure of its components is introduced, while for the latter one an explicit formula for determining the corresponding quantities is proved. A numerical investigation is carried out by the aid of the theoretical outcomes of the manuscript and some concluding remarks about the design parameters of the underlying systems are also discussed.

Suggested Citation

  • Ioannis S. Triantafyllou, 2024. "On the importance measures of Markov chain imbeddable reliability systems: some advances for k-out-of-n: G and consecutive-k-out-of-n: G structures," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(4), pages 1434-1443, April.
    • Handle: RePEc:spr:ijsaem:v:15:y:2024:i:4:d:10.1007_s13198-023-01903-6
    DOI: 10.1007/s13198-023-01903-6
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    References listed on IDEAS

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    1. Anshul Gupta & Pravin Srinath, 2022. "A recommender system based on collaborative filtering, graph theory using HMM based similarity measures," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(1), pages 533-545, March.
    2. Soni Bisht & Akshay Kumar & Nupur Goyal & Mangey Ram & Yury Klochkov, 2021. "Analysis of Network Reliability Characteristics and Importance of Components in a Communication Network," Mathematics, MDPI, vol. 9(12), pages 1-13, June.
    3. Aleksandr V. Zazhigalkin & Iosif Z. Aronov & Olga V. Maksimova & Ljubisa Papic, 2019. "Control of consensus convergence in technical committees of standardization on the basis of regular Markov chains model," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(1), pages 29-36, November.
    4. Stathis Chadjiconstantinidis & Markos V. Koutras, 1999. "Measures of component importance for markov chain imbeddable reliability structures," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(6), pages 613-639, September.
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