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On Reliability Function of a k -out-of- n System with Decreasing Residual Lifetime of Surviving Components after Their Failures

Author

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  • Vladimir Rykov

    (Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., 117198 Moscow, Russia
    Department of Applied Mathematics and Computer Modelling, National University of Oil and Gas “Gubkin University”, 65 Leninsky Prospect, 119991 Moscow, Russia
    Institute for Transmission Information Problems (Named after A.A. Kharkevich) RAS, Bolshoy Karetny, 19, GSP-4, 127051 Moscow, Russia)

  • Nika Ivanova

    (Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., 117198 Moscow, Russia
    V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya Str., 117997 Moscow, Russia)

  • Dmitry Kozyrev

    (Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., 117198 Moscow, Russia
    V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya Str., 117997 Moscow, Russia)

  • Tatyana Milovanova

    (Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., 117198 Moscow, Russia)

Abstract

We consider the reliability function of a k -out-of- n system under conditions that failures of its components lead to an increase in the load on the remaining ones and, consequently, to a change in their residual lifetimes. Development of models able to take into account that failures of a system’s components lead to a decrease in the residual lifetime of the surviving ones is of crucial significance in the system reliability enhancement tasks. This paper proposes a novel approach based on the application of order statistics of the system’s components lifetime to model this situation. An algorithm for calculation of the system reliability function and two moments of its uptime has been developed. Numerical study includes sensitivity analysis for special cases of the considered model based on two real-world systems. The results obtained show the sensitivity of system’s reliability characteristics to the shape of lifetime distribution, as well as to the value of its coefficient of variation at a fixed mean.

Suggested Citation

  • Vladimir Rykov & Nika Ivanova & Dmitry Kozyrev & Tatyana Milovanova, 2022. "On Reliability Function of a k -out-of- n System with Decreasing Residual Lifetime of Surviving Components after Their Failures," Mathematics, MDPI, vol. 10(22), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4243-:d:971296
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    References listed on IDEAS

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    1. Bairamov, Ismihan & Arnold, Barry C., 2008. "On the residual lifelengths of the remaining components in an n-k+1 out of n system," Statistics & Probability Letters, Elsevier, vol. 78(8), pages 945-952, June.
    2. Jorge Navarro & Marco Burkschat, 2011. "Coherent systems based on sequential order statistics," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(2), pages 123-135, March.
    3. Zdeněk Kala, 2021. "New Importance Measures Based on Failure Probability in Global Sensitivity Analysis of Reliability," Mathematics, MDPI, vol. 9(19), pages 1-20, September.
    4. Gregory Levitin, 2005. "The Universal Generating Function in Reliability Analysis and Optimization," Springer Series in Reliability Engineering, Springer, number 978-1-84628-245-4, June.
    5. Erhard Cramer & Udo Kamps, 1996. "Sequential order statistics and k-out-of-n systems with sequentially adjusted failure rates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 535-549, September.
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    Cited by:

    1. Vladimir Rykov & Olga Kochueva, 2023. "Preventive Maintenance of k -out-of- n System with Dependent Failures," Mathematics, MDPI, vol. 11(2), pages 1-17, January.

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