IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v251y2024ics0951832024004435.html
   My bibliography  Save this article

Reliability assessment of discrete-time k/n(G) retrial system based on different failure types and the δ-shock model

Author

Listed:
  • Hu, Zebin
  • Hu, Linmin
  • Wu, Shaomin
  • Yu, Xiaoyun

Abstract

The k/n(G) system is a typical reliability system in engineering practice. However, research on this system under discrete-time and retrial conditions is still limited. This paper establishes a k/n(G) retrial system model under a discrete-time condition based on different failure types and the δ-shock model, whose objective is to investigate its various reliability measures and the relationship between measures and parameters. Two methodologies are utilized in this paper to evaluate the system’s various measures: the analytical method for the discrete-time Markov process and the Monte Carlo simulation method. The two methodologies are compared, and optimization is performed on certain measures concerning system parameters. A discrete PH distribution representation method for component lifetime under the δ-shock is presented, the relationship between various reliability measures of the system and various parameters is determined, and a novel approach for system reliability research based on the discrete PH distribution and the δ-shock is provided in this paper.

Suggested Citation

  • Hu, Zebin & Hu, Linmin & Wu, Shaomin & Yu, Xiaoyun, 2024. "Reliability assessment of discrete-time k/n(G) retrial system based on different failure types and the δ-shock model," Reliability Engineering and System Safety, Elsevier, vol. 251(C).
    • Handle: RePEc:eee:reensy:v:251:y:2024:i:c:s0951832024004435
    DOI: 10.1016/j.ress.2024.110371
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832024004435
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2024.110371?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. Cihangir Kan & Serkan Eryilmaz, 2021. "Reliability assessment of a discrete time cold standby repairable system," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 613-628, October.
    2. Yen, Tseng-Chang & Wang, Kuo-Hsiung, 2020. "Cost benefit analysis of four retrial systems with warm standby units and imperfect coverage," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    3. Davies, Katherine & Dembińska, Anna, 2019. "On the number of failed components in a k-out-of-n system upon system failure when the lifetimes are discretely distributed," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 47-61.
    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. Yi Jiang, 2020. "A new δ-shock model for systems subject to multiple failure types and its optimal order-replacement policy," Journal of Risk and Reliability, , vol. 234(1), pages 138-150, February.
    6. Guo, Yongjin & Zhong, Mingjun & Gao, Chao & Wang, Hongdong & Liang, Xiaofeng & Yi, Hong, 2021. "A discrete-time Bayesian network approach for reliability analysis of dynamic systems with common cause failures," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    7. 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).
    8. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2023. "Optimal aborting policy for shock exposed missions with random rescue time," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    9. Srinivas R. Chakravarthy & A. Krishnamoorthy & P. V. Ushakumari, 2001. "A k -out-of- n reliability system with an unreliable server and phase type repairs and services: the ( N , T ) policy," International Journal of Stochastic Analysis, Hindawi, vol. 14, pages 1-20, January.
    10. Lyu, Hao & Qu, Hongchen & Xie, Hualong & Zhang, Yimin & Pecht, Michael, 2023. "Reliability analysis of the multi-state system with nonlinear degradation model under Markov environment," Reliability Engineering and System Safety, Elsevier, vol. 238(C).
    11. Eryilmaz, Serkan & Unlu, Kamil Demirberk, 2023. "A new generalized δ-shock model and its application to 1-out-of-(m+1):G cold standby system," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    12. Gao, Shan & Wang, Jinting, 2021. "Reliability and availability analysis of a retrial system with mixed standbys and an unreliable repair facility," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    13. Ruiz-Castro, Juan Eloy & Fernández-Villodre, Gemma, 2012. "A complex discrete warm standby system with loss of units," European Journal of Operational Research, Elsevier, vol. 218(2), pages 456-469.
    14. Cirillo, Pasquale & Hüsler, Jürg, 2011. "Extreme shock models: An alternative perspective," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 25-30, January.
    15. Wang, Xiaoyue & Zhao, Xian & Wang, Siqi & Sun, Leping, 2020. "Reliability and maintenance for performance-balanced systems operating in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    16. A. Krishnamoorthy & P. Ushakumari, 1999. "Reliability of ak-out-of-n system with repair and retrial of failed units," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 293-304, December.
    17. Xiahou, Tangfan & Zheng, Yi-Xuan & Liu, Yu & Chen, Hong, 2023. "Reliability modeling of modular k-out-of-n systems with functional dependency: A case study of radar transmitter systems," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    18. Wu, Congshan & Zhao, Xian & Qiu, Qingan & Sun, Jinglei, 2021. "Optimal mission abort policy for k-out-of-n: F balanced systems," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    19. Shamstabar, Yousof & Shahriari, Hamid & Samimi, Yaser, 2021. "Reliability monitoring of systems with cumulative shock-based deterioration process," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    20. Zhang, Jinchun & Lv, Hang & Hou, Jinxiu, 2023. "A novel general model for RAP and RRAP optimization of k-out-of-n:G systems with mixed redundancy strategy," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    21. Xu, Dong & Tian, Yubin & Shi, Junbiao & Wang, Dianpeng & Zhang, Ming & Li, Haijin, 2023. "Reliability analysis and optimal redundancy for a satellite power supply system based on a new dynamic k-out-of-n: G model," Reliability Engineering and System Safety, Elsevier, vol. 236(C).
    22. Juan Eloy Ruiz-Castro, 2015. "A preventive maintenance policy for a standby system subject to internal failures and external shocks with loss of units," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(9), pages 1600-1613, July.
    23. 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).
    24. Linmin Hu & Sijia Liu & Rui Peng & Zhaocai Liu, 2022. "Reliability and sensitivity analysis of a repairable k-out-of-n:G system with two failure modes and retrial feature," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(9), pages 3043-3064, March.
    25. Yang, Dong-Yuh & Tsao, Chih-Lung, 2019. "Reliability and availability analysis of standby systems with working vacations and retrial of failed components," Reliability Engineering and System Safety, Elsevier, vol. 182(C), pages 46-55.
    26. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2024. "Allocation and activation of resource constrained shock-exposed components in heterogeneous 1-out-of-n standby system," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    27. 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).
    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. 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).
    2. Changjiang Lai & Ehmet Kasim & Ahmadjan Muhammadhaji, 2024. "Dynamic Analysis of a Standby System with Retrial Strategies and Multiple Working Vacations," Mathematics, MDPI, vol. 12(24), pages 1-34, December.
    3. 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).
    4. Li, Mingjia & Hu, Linmin & Peng, Rui & Bai, Zhuoxin, 2021. "Reliability modeling for repairable circular consecutive-k-out-of-n: F systems with retrial feature," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    5. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2024. "Optimizing corrective maintenance for multistate systems with storage," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    6. Jiang, Shan & Jia, Xujie, 2024. "Reliability assessment under continuous fatigue degradation and shock based on Markov renewal process," Reliability Engineering and System Safety, Elsevier, vol. 248(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. Kang, Fengming & Cui, Lirong & Ye, Zhisheng & Zhou, Yu, 2024. "Reliability analysis for systems with self-healing mechanism in degradation-shock dependence processes with changing degradation rate," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    9. 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).
    10. Wu, Chia-Huang & Yen, Tseng-Chang & Wang, Kuo-Hsiung, 2021. "Availability and Comparison of Four Retrial Systems with Imperfect Coverage and General Repair Times," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    11. Oszczypała, Mateusz & Konwerski, Jakub & Ziółkowski, Jarosław & Małachowski, Jerzy, 2024. "Reliability analysis and redundancy optimization of k-out-of-n systems with random variable k using continuous time Markov chain and Monte Carlo simulation," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    12. 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).
    13. Yang, Shunkun & Shao, Qi & Bian, Chong, 2022. "Reliability analysis of ensemble fault tolerance for soft error mitigation against complex radiation effect," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    14. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2024. "Optimal system loading and aborting in additive multi-attempt missions," Reliability Engineering and System Safety, Elsevier, vol. 251(C).
    15. Meng, Sa & Xing, Liudong & Levitin, Gregory, 2024. "Optimizing component activation and operation aborting in missions with consecutive attempts and common abort command," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    16. 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).
    17. Liu, Lujie & Yang, Jun & Yan, Bingxin, 2024. "A dynamic mission abort policy for transportation systems with stochastic dependence by deep reinforcement learning," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    18. Wang, Kuo-Hsiung & Wu, Chia-Huang & Yen, Tseng-Chang, 2022. "Comparative cost-benefit analysis of four retrial systems with preventive maintenance and unreliable service station," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    19. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2024. "A new self-adaptive mission aborting policy for systems operating in uncertain random shock environment," Reliability Engineering and System Safety, Elsevier, vol. 248(C).
    20. Ruiz-Castro, Juan Eloy & Dawabsha, Mohammed & Alonso, Francisco Javier, 2018. "Discrete-time Markovian arrival processes to model multi-state complex systems with loss of units and an indeterminate variable number of repairpersons," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 114-127.

    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:eee:reensy:v:251:y:2024:i:c:s0951832024004435. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    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.