IDEAS home Printed from https://ideas.repec.org/a/spr/operea/v25y2025i2d10.1007_s12351-025-00931-3.html
   My bibliography  Save this article

Reliability evaluation and simulation of shock model for repairable retrial systems with $$N$$ N -policy

Author

Listed:
  • Jian Liu

    (Yanshan University)

  • Linmin Hu

    (Yanshan University)

  • Yiyan Zhou

    (Yanshan University)

Abstract

System design based on retrial mechanism has extensive applications in the field of computer networks, and the N-policy is a crucial maintenance strategy in the design of repairable system. The impact of external shocks is unavoidable for network communication systems. Based on such actual situations, this paper proposes a shock model for a repairable $$k$$ k -out-of- $$n$$ n :G retrial systems with the N-policy. Component failure is caused by both self-degradation and external shocks. The shock may cause multiple component failures at the same time. Based on stochastic process theory, state probability equations of the system are constructed, and steady-state indexes and the state probabilities of the system are evaluated. A simulation algorithm for the developed shock model is proposed, by utilizing the Monte Carlo method. The running process of the system is simulated by numerical experiments, and the analytical solutions of the system steady-state indexes are compared with the simulated values. In order to show the influence of different parameters on the steady-state indexes, the sensitivity analysis is conducted on system availability and the number of operating components. Based on the constructed system cost function, the optimal number of operating components and the optimal N-policy value of the system are analyzed and determined.

Suggested Citation

  • Jian Liu & Linmin Hu & Yiyan Zhou, 2025. "Reliability evaluation and simulation of shock model for repairable retrial systems with $$N$$ N -policy," Operational Research, Springer, vol. 25(2), pages 1-35, June.
    • Handle: RePEc:spr:operea:v:25:y:2025:i:2:d:10.1007_s12351-025-00931-3
    DOI: 10.1007/s12351-025-00931-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12351-025-00931-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s12351-025-00931-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ranjkesh, Somayeh Hamed & Hamadani, Ali Zeinal & Mahmoodi, Safieh, 2019. "A new cumulative shock model with damage and inter-arrival time dependency," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
    2. Eryilmaz, Serkan & Kan, Cihangir, 2019. "Reliability and optimal replacement policy for an extreme shock model with a change point," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    3. Ning, Ru & Wang, Xiaoyue & Zhao, Xian & Li, Ziyue, 2024. "Joint optimization of preventive maintenance and triggering mechanism for k-out-of-n: F systems with protective devices based on periodic inspection," Reliability Engineering and System Safety, Elsevier, vol. 251(C).
    4. Juybari, Mohammad N. & Hamadani, Ali Zeinal & Ardakan, Mostafa Abouei, 2023. "Availability analysis and cost optimization of a repairable system with a mix of active and warm-standby components in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    5. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2021. "Optimal shock-driven switching strategies with elements reuse in heterogeneous warm-standby systems," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    6. Baoliang Liu & Yanqing Wen & Shugui Kang & Qingan Qiu, 2020. "A multiple warm standby repairable system under N-policy with multiple vacations following Markovian arrival process," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(15), pages 3609-3634, August.
    7. Meena, Rakesh Kumar & Jain, Madhu & Assad, Assif & Sethi, Rachita & Garg, Deepika, 2022. "Performance and cost comparative analysis for M/G/1 repairable machining system with N-policy vacation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 315-328.
    8. 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).
    9. Jing Li & Linmin Hu & Yuyu Wang & Jia Kang, 2024. "Reliability analysis and optimization design of a repairable k-out-of-n retrial system with two failure modes and preventive maintenance," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(15), pages 5524-5552, August.
    10. Fang Luo & Linmin Hu & Yuyu Wang & Xiaoyun Yu, 2024. "Statistical inference of reliability for a K-out-of-N: G system with switching failure under Poisson shocks," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 8(3), pages 195-210, July.
    11. Stathis Chadjiconstantinidis & Serkan Eryilmaz, 2022. "Reliability Assessment for Censored $${\boldsymbol{\delta}}$$ δ -Shock Models," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3141-3173, December.
    12. Eryilmaz, Serkan, 2024. "Reliability and performance evaluation of weighted k-out-of-n:G system consisting of components with discrete lifetimes," Reliability Engineering and System Safety, Elsevier, vol. 252(C).
    13. CheSoong Kim & Sergey Dudin, 2012. "A multi-server queueing model with retrial connection arrivals as a model for optimisation of the traffic control," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(8), pages 1555-1567.
    14. Jau-Chuan Ke & Chia-Huang Wu & Wen Lea Pearn, 2011. "Multi-server retrial queue with second optional service: algorithmic computation and optimisation," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(10), pages 1755-1769.
    15. Madhu Jain & Ritu Gupta, 2018. "N-policy for redundant repairable system with multiple types of warm standbys with switching failure and vacation," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 13(4), pages 419-449.
    16. 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).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Juybari, Mohammad N. & Hamadani, Ali Zeinal & Ardakan, Mostafa Abouei, 2023. "Availability analysis and cost optimization of a repairable system with a mix of active and warm-standby components in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    2. Yu, Xiaoyun & Hu, Linmin & Ma, Mengrao, 2023. "Reliability measures of discrete time k-out-of-n: G retrial systems based on Bernoulli shocks," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    3. Qi Shao & Linmin Hu & Fan Xu, 2024. "Reliability and Optimization for k-out-of-n: G Mixed Standby Retrial System with Dependency and J-Vacation," Methodology and Computing in Applied Probability, Springer, vol. 26(1), pages 1-27, March.
    4. Lyu, Hao & Qu, Hongchen & Yang, Zaiyou & Ma, Li & Lu, Bing & Pecht, Michael, 2023. "Reliability analysis of dependent competing failure processes with time-varying δ shock model," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    5. Levitin, Gregory & Xing, Liudong & Dai, Yanshun, 2022. "Minimum cost replacement and maintenance scheduling in dual-dissimilar-unit standby systems," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    6. Zhao, Xian & Dong, Bingbing & Wang, Xiaoyue, 2023. "Reliability analysis of a two-dimensional voting system equipped with protective devices considering triggering failures," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    7. Xiaoyue Wang & Ru Ning & Xian Zhao, 2023. "Generalized mixed shock model for multi-component systems in the shock environment with a change point," Journal of Risk and Reliability, , vol. 237(4), pages 619-635, August.
    8. Wang, Xiaoyue & Ning, Ru & Zhao, Xian & Zhou, Jian, 2022. "Reliability analyses of k-out-of-n: F capability-balanced systems in a multi-source shock environment," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    9. Zhang, Changzhen & Yang, Jun & Li, Mingjia & Wang, Ning, 2024. "Reliability analysis of a two-dimensional linear consecutive-(r,s)-out-of-(m,n): F repairable system," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    10. Liu, Baoliang & Wen, Yanqing & Qiu, Qingan & Shi, Haiyan & Chen, Jianhui, 2022. "Reliability analysis for multi-state systems under K-mixed redundancy strategy considering switching failure," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    11. Mohsen Bohlooli-Zefreh & Afshin Parvardeh & Majid Asadi, 2023. "On the occurrence time of an extreme damage in a general shock model," Journal of Risk and Reliability, , vol. 237(6), pages 1100-1113, December.
    12. Xu, Qinqin & Zhu, Yuanguo, 2022. "Reliability modeling of uncertain random fractional differential systems with competitive failures," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    13. Zhao, Xian & Qi, Xin & Wang, Xiaoyue, 2023. "Reliability assessment for coherent systems operating under a generalized mixed shock model with multiple change points of the environment," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    14. Wang, Xiaoyue & Zhao, Xian & Wu, Congshan & Wang, Siqi, 2022. "Mixed shock model for multi-state weighted k-out-of-n: F systems with degraded resistance against shocks," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    15. Levitin, Gregory & Xing, Liudong & Xiang, Yanping, 2021. "Optimal multiple replacement and maintenance scheduling in two-unit systems," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    16. Xian Zhao & Rong Li & Yu Fan & Qingan Qiu, 2022. "Reliability modeling for multi-state systems with a protective device considering multiple triggering mechanism," Journal of Risk and Reliability, , vol. 236(1), pages 173-193, February.
    17. Chadjiconstantinidis, Stathis & Eryilmaz, Serkan, 2023. "Reliability of a mixed δ-shock model with a random change point in shock magnitude distribution and an optimal replacement policy," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    18. Levitin, Gregory & Xing, Liudong & Dai, Yanshun, 2021. "Joint optimal mission aborting and replacement and maintenance scheduling in dual-unit standby systems," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    19. Jain, Madhu & Kumar, Pankaj & Singh, Mayank & Gupta, Ritu, 2024. "Cost optimization and reliability analysis of fault tolerant system with service interruption and reboot," Reliability Engineering and System Safety, Elsevier, vol. 249(C).
    20. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2021. "Influence of storage on mission success probability of m-out-of-n standby systems with reusable elements," Reliability Engineering and System Safety, Elsevier, vol. 216(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:operea:v:25:y:2025:i:2:d:10.1007_s12351-025-00931-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.