IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v232y2023ics0951832022006950.html
   My bibliography  Save this article

Reliability of a mixed δ-shock model with a random change point in shock magnitude distribution and an optimal replacement policy

Author

Listed:
  • Chadjiconstantinidis, Stathis
  • Eryilmaz, Serkan

Abstract

A mixed δ-shock model when there is a change in the distribution of the magnitudes of shocks is defined and studied. Such a model which is a combination of the δ-shock model and the extreme shock model with a random change point (studied by Eryilmaz and Kan, 2019), is useful in practice since a sudden change in environmental conditions may cause a larger shock. In particular, the reliability and the mean time to failure of the system are evaluated by assuming that the random change point has a discrete phase-type distribution. Analytical results for evaluating the reliability function of the system for several joint distributions of the interarrival times and the magnitudes of shocks, are also given. The optimal replacement policy that is based on a control limit is also proposed when the number of shocks until the change point follows geometric distribution. The results are illustrated by numerical examples.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:reensy:v:232:y:2023:i:c:s0951832022006950
    DOI: 10.1016/j.ress.2022.109080
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832022006950
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2022.109080?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. Dheeraj Goyal & Nil Kamal Hazra & Maxim Finkelstein, 2022. "On the Time-Dependent Delta-Shock Model Governed by the Generalized PóLya Process," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1627-1650, September.
    2. Huang, Xianzhen & Jin, Sujun & He, Xuefeng & He, David, 2019. "Reliability analysis of coherent systems subject to internal failures and external shocks," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 75-83.
    3. Levitin, Gregory & Finkelstein, Maxim & Huang, Hong-Zhong, 2019. "Scheduling of imperfect inspections for reliability critical systems with shock-driven defects and delayed failures," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 89-98.
    4. 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).
    5. Rafiee, Koosha & Feng, Qianmei & Coit, David W., 2017. "Reliability assessment of competing risks with generalized mixed shock models," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 1-11.
    6. Cha, Ji Hwan & Finkelstein, Maxim & Levitin, Gregory, 2017. "On preventive maintenance of systems with lifetimes dependent on a random shock process," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 90-97.
    7. Mohammad Hossein Poursaeed, 2021. "Reliability analysis of an extended shock model," Journal of Risk and Reliability, , vol. 235(5), pages 845-852, October.
    8. 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).
    9. Jorge Navarro & Pedro Hernandez, 2008. "Mean residual life functions of finite mixtures, order statistics and coherent systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 277-298, April.
    10. 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.
    11. Coskun Kus & Altan Tuncel & Serkan Eryilmaz, 2022. "Assessment of Shock Models for a Particular Class of Intershock Time Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 213-231, March.
    12. Zhao, Bing & Yue, Dequan & Liao, Haitao & Liu, Yuanhui & Zhang, Xiaohong, 2021. "Performance analysis and optimization of a cold standby system subject to δ-shocks and imperfect repairs," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    13. Li, Zehui & Kong, Xinbing, 2007. "Life behavior of [delta]-shock model," Statistics & Probability Letters, Elsevier, vol. 77(6), pages 577-587, March.
    14. Wu, Bei & Cui, Lirong, 2020. "Reliability evaluation of Markov renewal shock models with multiple failure mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    15. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "New shock models based on the generalized Polya process," European Journal of Operational Research, Elsevier, vol. 251(1), pages 135-141.
    16. Alkaff, Abdullah, 2021. "Discrete time dynamic reliability modeling for systems with multistate components," Reliability Engineering and System Safety, Elsevier, vol. 209(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2024. "Optimizing corrective maintenance for multistate systems with storage," Reliability Engineering and System Safety, Elsevier, vol. 244(C).
    2. 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).
    3. Chadjiconstantinidis, Stathis & Eryilmaz, Serkan, 2024. "On δ-shock model with a change point in intershock time distribution," Statistics & Probability Letters, Elsevier, vol. 208(C).
    4. 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).

    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. 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).
    2. 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).
    3. 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).
    4. 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).
    5. 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).
    6. Chadjiconstantinidis, Stathis & Eryilmaz, Serkan, 2024. "On δ-shock model with a change point in intershock time distribution," Statistics & Probability Letters, Elsevier, vol. 208(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. Wei, Xiaohua & Bai, Sijun & Wu, Bei, 2023. "A novel shock-dependent preventive maintenance policy for degraded systems subject to dynamic environments and N-critical shocks," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    10. 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).
    11. 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.
    12. Wu, Bei & Wei, Xiaohua & Zhang, Yamei & Bai, Sijun, 2023. "Modeling dynamic environment effects on dependent failure processes with varying failure thresholds," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    13. Zhao, Xian & He, Zongda & Wu, Yaguang & Qiu, Qingan, 2022. "Joint optimization of condition-based performance control and maintenance policies for mission-critical systems," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    14. Lina Bian & Bo Peng & Yong Ye, 2023. "Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Pólya Censored δ Shock Model," Mathematics, MDPI, vol. 11(21), pages 1-19, November.
    15. Zhao, Xian & Guo, Xiaoxin & Wang, Xiaoyue, 2018. "Reliability and maintenance policies for a two-stage shock model with self-healing mechanism," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 185-194.
    16. Stathis Chadjiconstantinidis & Altan Tuncel & Serkan Eryilmaz, 2023. "Α new mixed δ-shock model with a change in shock distribution," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 491-509, October.
    17. Ye, Kewei & Wang, Han & Ma, Xiaobing, 2023. "A generalized dynamic stress-strength interference model under δ-failure criterion for self-healing protective structure," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    18. Asadi, Majid, 2023. "On a parametric model for the mean number of system repairs with applications," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    19. Zarezadeh, Somayeh & Ashrafi, Somayeh, 2019. "On preventive maintenance of networks with components subject to external shocks," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    20. 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.

    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:232:y:2023:i:c:s0951832022006950. 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.