IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v65y2018i4p347-359.html
   My bibliography  Save this article

On total capacity of k‐out‐of‐n systems with random weights

Author

Listed:
  • Yiying Zhang
  • Weiyong Ding
  • Peng Zhao

Abstract

In engineering applications, many reliability systems can be modeled as k‐out‐of‐n systems with components having random weights. Before putting such kind of system into a working state, it is of great significance for a system designer to find out the optimal assembly of the random weights to the components. In this article, we investigate the performance levels of k‐out‐of‐n systems with random weights. Optimal assembly policies are obtained by maximizing the total capacity according to different criteria, including the usual stochastic order, the increasing convex [concave] order, and the expectation order. Based on the optimal assembly strategy derived by maximizing the expected total capacity, we further investigate stochastic properties of the resulting weighted system with respect to the vector of expectations of random weights. Numerical examples are provided to highlight our theoretical findings as well.

Suggested Citation

  • Yiying Zhang & Weiyong Ding & Peng Zhao, 2018. "On total capacity of k‐out‐of‐n systems with random weights," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(4), pages 347-359, June.
    • Handle: RePEc:wly:navres:v:65:y:2018:i:4:p:347-359
    DOI: 10.1002/nav.21810
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.21810
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.21810?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
    ---><---

    References listed on IDEAS

    as
    1. Zhang, Yiying & Zhao, Peng, 2015. "Comparisons on aggregate risks from two sets of heterogeneous portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 124-135.
    2. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    3. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    4. Cai, Jun & Wei, Wei, 2015. "Notions of multivariate dependence and their applications in optimal portfolio selections with dependent risks," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 156-169.
    5. You, Yinping & Li, Xiaohu, 2015. "Functional characterizations of bivariate weak SAI with an application," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 225-231.
    6. Zhang, Yiying, 2018. "Optimal allocation of active redundancies in weighted k-out-of-n systems," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 110-117.
    7. Eryilmaz, Serkan, 2013. "On reliability analysis of a k-out-of-n system with components having random weights," Reliability Engineering and System Safety, Elsevier, vol. 109(C), pages 41-44.
    8. Samaniego, Francisco J. & Shaked, Moshe, 2008. "Systems with weighted components," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 815-823, April.
    9. Cai, Jun & Wei, Wei, 2014. "Some new notions of dependence with applications in optimal allocation problems," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 200-209.
    10. Rahmani, Rabi-Allah & Izadi, Muhyiddin & Khaledi, Baha-Eldin, 2016. "Stochastic comparisons of total capacity of weighted-k-out-of-n systems," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 216-220.
    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. Zhang, Yiying, 2021. "Reliability Analysis of Randomly Weighted k-out-of-n Systems with Heterogeneous Components," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    2. Eryilmaz, Serkan & Ucum, Kaan Ayberk, 2021. "The lost capacity by the weighted k-out-of-n system upon system failure," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    3. Hamdan, K. & Tavangar, M. & Asadi, M., 2021. "Optimal preventive maintenance for repairable weighted k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 205(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. Zhang, Yiying & Cheung, Ka Chun, 2020. "On the increasing convex order of generalized aggregation of dependent random variables," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 61-69.
    2. Yinping You & Xiaohu Li & Rui Fang, 2021. "On coverage limits and deductibles for SAI loss severities," Annals of Operations Research, Springer, vol. 297(1), pages 341-357, February.
    3. Li, Chen & Li, Xiaohu, 2019. "Preservation of WSAI under default transforms and its application in allocating assets with dependent realizable returns," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 84-91.
    4. Hamdan, K. & Tavangar, M. & Asadi, M., 2021. "Optimal preventive maintenance for repairable weighted k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    5. Eryilmaz, Serkan & Ucum, Kaan Ayberk, 2021. "The lost capacity by the weighted k-out-of-n system upon system failure," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    6. Zhang, Yiying, 2021. "Reliability Analysis of Randomly Weighted k-out-of-n Systems with Heterogeneous Components," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    7. Pan Xiaoqing & Li Xiaohu, 2017. "On capital allocation for stochastic arrangement increasing actuarial risks," Dependence Modeling, De Gruyter, vol. 5(1), pages 145-153, January.
    8. Li, Chen & Li, Xiaohu, 2017. "Preservation of weak stochastic arrangement increasing under fixed time left-censoring," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 42-49.
    9. Serkan Eryilmaz & Ali Riza Bozbulut, 2019. "Reliability analysis of weighted- k -out-of- n system consisting of three-state components," Journal of Risk and Reliability, , vol. 233(6), pages 972-977, December.
    10. Li, Chen & Li, Xiaohu, 2016. "Sufficient conditions for ordering aggregate heterogeneous random claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 406-413.
    11. Li, Chen & Li, Xiaohu, 2020. "Preservation of weak SAI’s under increasing transformations with applications," Statistics & Probability Letters, Elsevier, vol. 164(C).
    12. Cai, Jun & Wei, Wei, 2015. "Notions of multivariate dependence and their applications in optimal portfolio selections with dependent risks," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 156-169.
    13. Dimitrios G. Konstantinides & Georgios C. Zachos, 2019. "Exhibiting Abnormal Returns Under a Risk Averse Strategy," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 551-566, June.
    14. Zheng, Yanting & Yang, Jingping & Huang, Jianhua Z., 2011. "Approximation of bivariate copulas by patched bivariate Fréchet copulas," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 246-256, March.
    15. Said Khalil, 2022. "Expectile-based capital allocation," Working Papers hal-03816525, HAL.
    16. Denuit, Michel & Hieber, Peter & Robert, Christian Y., 2021. "Mortality credits within large survivor funds," LIDAM Discussion Papers ISBA 2021038, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Nam, Hee Seok & Tang, Qihe & Yang, Fan, 2011. "Characterization of upper comonotonicity via tail convex order," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 368-373, May.
    18. Kaas, Rob & Tang, Qihe, 2005. "A large deviation result for aggregate claims with dependent claim occurrences," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 251-259, June.
    19. Wenjun Jiang & Jiandong Ren & Ričardas Zitikis, 2017. "Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account," Risks, MDPI, vol. 5(1), pages 1-22, February.
    20. He, Junnan & Tang, Qihe & Zhang, Huan, 2016. "Risk reducers in convex order," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 80-88.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:65:y:2018:i:4:p:347-359. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.