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The reliability of a generalized consecutive system

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  • Dafnis, Spiros D.
  • Makri, Frosso S.
  • Philippou, Andreas N.

Abstract

In the present paper we introduce a modified consecutive system, which generalizes consecutive systems extensively studied in the literature, and we obtain its reliability when its components are functioning independently with probabilities not necessarily equal. The results are illustrated by numerical examples using MATLAB and potential applications are discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:359:y:2019:i:c:p:186-193
    DOI: 10.1016/j.amc.2019.04.056
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    References listed on IDEAS

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    1. 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.
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    3. Francisco J. Samaniego, 2007. "System Signatures and their Applications in Engineering Reliability," International Series in Operations Research and Management Science, Springer, number 978-0-387-71797-5, December.
    4. Spiros Dafnis & Andreas Philippou & Demetrios Antzoulakos, 2012. "Distributions of patterns of two successes separated by a string of k-2 failures," Statistical Papers, Springer, vol. 53(2), pages 323-344, May.
    5. D. Antzoulakos & S. Bersimis & M. Koutras, 2003. "On the distribution of the total number of run lengths," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(4), pages 865-884, December.
    6. Philippou, Andreas N. & Makri, Frosso S., 1986. "Successes, runs and longest runs," Statistics & Probability Letters, Elsevier, vol. 4(4), pages 211-215, June.
    7. Kiyoshi Inoue, 2004. "Joint distributions associated with patterns, successes and failures in a sequence of multi-state trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(1), pages 143-168, March.
    8. M. Koutras & V. Alexandrou, 1995. "Runs, scans and URN model distributions: A unified Markov chain approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(4), pages 743-766, December.
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    Cited by:

    1. 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.
    2. Ioannis S. Triantafyllou & Miltiadis Chalikias, 2023. "Consecutive- k 1 and k 2 -out-of- n : F Structures with a Single Change Point," Stats, MDPI, vol. 6(1), pages 1-12, March.
    3. Spiros D. Dafnis & Frosso S. Makri & Markos V. Koutras, 2021. "Generalizations of Runs and Patterns Distributions for Sequences of Binary Trials," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 165-185, March.
    4. 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).
    5. Spiros D. Dafnis & Frosso S. Makri, 2022. "Weak runs in sequences of binary trials," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(5), pages 573-603, July.
    6. Ioannis S. Triantafyllou, 2020. "On the Consecutive k 1 and k 2 -out-of- n Reliability Systems," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
    7. Wang, Yan & Hu, Linmin & Yang, Li & Li, Jing, 2022. "Reliability modeling and analysis for linear consecutive-k-out-of-n: F retrial systems with two maintenance activities," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    8. Marilena Jianu & Leonard Dăuş & Vlad-Florin Drăgoi & Valeriu Beiu, 2023. "The Roots of the Reliability Polynomials of Circular Consecutive- k -out-of- n :F Systems," Mathematics, MDPI, vol. 11(20), pages 1-12, October.

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