IDEAS home Printed from https://ideas.repec.org/a/taf/uiiexx/v49y2017i7p722-736.html
   My bibliography  Save this article

A linear weighted system for non-homogeneous Markov-dependent components

Author

Listed:
  • Xiaoyan Zhu
  • Mahmoud Boushaba

Abstract

We study a linear weighted (n, f, k) system, denoted by L(n, f, k, w) system and consider the situation where components are non-homogeneous Markov-dependent. An L(n, f, k, w) system consists of n components ordered in a line, and each component u has a positive integer weight wu for u = 1, 2, …, n and w = (w1, w2, …, wn). The L(n, f, k, w):F (G) system fails (works) if the total weight of failed (working) components is at least f or the total weight of consecutive failed (working) components is at least k. For the L(n, f, k, w):F system with non-homogeneous Markov-dependent components, we derive closed-form formulas for the system reliability, the marginal reliability importance measure of a single component, and the joint reliability importance measure of multiple components using a conditional probability generating function method. We extend these results to the L(n, f, k, w):G systems, the weighted consecutive-k-out-of-n systems, and the weighted f-out-of-n systems. Our numerical examples and a case study on a bridge system demonstrate the use of derived formulas and provide the insights on the L(n, f, k, w) systems and the importance measures. In addition, the two failure modes associated with the L(n, f, k, w):F systems are analyzed by comparing to the single failure mode associated with the weighted consecutive-k-out-of-n:F systems and the single failure mode associated with the weighted f-out-of-n:F systems.

Suggested Citation

  • Xiaoyan Zhu & Mahmoud Boushaba, 2017. "A linear weighted system for non-homogeneous Markov-dependent components," IISE Transactions, Taylor & Francis Journals, vol. 49(7), pages 722-736, July.
  • Handle: RePEc:taf:uiiexx:v:49:y:2017:i:7:p:722-736
    DOI: 10.1080/24725854.2016.1269977
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/24725854.2016.1269977
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/24725854.2016.1269977?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. Xiaoyan Zhu & Qingzhu Yao & Way Kuo, 2012. "Patterns of the Birnbaum importance in linear consecutive--out-of- systems," IISE Transactions, Taylor & Francis Journals, vol. 44(4), pages 277-290.
    2. Qingzhu Yao & Xiaoyan Zhu & Way Kuo, 2011. "Heuristics for component assignment problems based on the Birnbaum importance," IISE Transactions, Taylor & Francis Journals, vol. 43(9), pages 633-646.
    3. K. K. Kamalja & R. L. Shinde, 2014. "On the Reliability of (n, f, k) and 〈n, f, k〉 Systems," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(8), pages 1649-1665, April.
    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. Zhu, Xiaoyan & Boushaba, Mahmoud & Coit, David W. & Benyahia, Azzeddine, 2017. "Reliability and importance measures for m-consecutive-k, l-out-of-n system with non-homogeneous Markov-dependent components," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 1-9.
    2. Xiaoyan Zhu & Mahmoud Boushaba & Abdelmoumene Boulahia & Xian Zhao, 2019. "A linear m-consecutive-k-out-of-n system with sparse d of non-homogeneous Markov-dependent components," Journal of Risk and Reliability, , vol. 233(3), pages 328-337, June.

    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. Xiaoyan Zhu & Mahmoud Boushaba & Abdelmoumene Boulahia & Xian Zhao, 2019. "A linear m-consecutive-k-out-of-n system with sparse d of non-homogeneous Markov-dependent components," Journal of Risk and Reliability, , vol. 233(3), pages 328-337, June.
    2. Qingzhu Yao & Xiaoyan Zhu & Way Kuo, 2014. "A Birnbaum-importance based genetic local search algorithm for component assignment problems," Annals of Operations Research, Springer, vol. 212(1), pages 185-200, January.
    3. Si, Shubin & Levitin, Gregory & Dui, Hongyan & Sun, Shudong, 2014. "Importance analysis for reconfigurable systems," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 72-80.
    4. Xiaoyan Zhu & Way Kuo, 2014. "Importance measures in reliability and mathematical programming," Annals of Operations Research, Springer, vol. 212(1), pages 241-267, January.
    5. Zhu, Xiaoyan & Boushaba, Mahmoud & Coit, David W. & Benyahia, Azzeddine, 2017. "Reliability and importance measures for m-consecutive-k, l-out-of-n system with non-homogeneous Markov-dependent components," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 1-9.
    6. Serkan Eryilmaz, 2013. "Component importance for linear consecutive‐ k ‐Out‐of‐ n and m ‐Consecutive‐ k ‐Out‐of‐ n systems with exchangeable components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(4), pages 313-320, June.
    7. Wang, Dan & Si, Shubin & Cai, Zhiqiang & Zhao, Jiangbin, 2021. "Reliability optimization of linear consecutive-k-out-of-n: F systems driven by reconfigurable importance," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    8. Liu, Mingli & Wang, Dan & Si, Shubin, 2023. "Mixed reliability importance-based solving algorithm design for the cost-constrained reliability optimization model," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    9. Fu, Yuqiang & Zhu, Xiaoyan & Ma, Xiaoyang, 2020. "Optimum component reallocation and system replacement maintenance for a used system with increasing minimal repair cost," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    10. Fu, Yuqiang & Zhu, Xiaoyan, 2023. "A joint age-based system replacement and component reallocation maintenance policy: Optimization, analysis and resilience," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    11. Liu, Bin & Xu, Zhengguo & Xie, Min & Kuo, Way, 2014. "A value-based preventive maintenance policy for multi-component system with continuously degrading components," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 83-89.
    12. K. K. Kamalja, 2017. "Markov binomial distribution of order k and its applications," Statistical Papers, Springer, vol. 58(3), pages 831-853, September.
    13. Cai, Zhiqiang & Si, Shubin & Sun, Shudong & Li, Caitao, 2016. "Optimization of linear consecutive-k-out-of-n system with a Birnbaum importance-based genetic algorithm," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 248-258.
    14. Fu, Yuqiang & Yuan, Tao & Zhu, Xiaoyan, 2019. "Importance-measure based methods for component reassignment problem of degrading components," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    15. Liu, Mingli & Wang, Dan & Zhao, Jiangbin & Si, Shubin, 2022. "Importance measure construction and solving algorithm oriented to the cost-constrained reliability optimization model," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    16. Qiu, Siqi & Ming, Xinguo & Sallak, Mohamed & Lu, Jialiang, 2022. "A Birnbaum importance-based two-stage approach for two-type component assignment problems," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    17. Zhao, Jiangbin & Si, Shubin & Cai, Zhiqiang, 2019. "A multi-objective reliability optimization for reconfigurable systems considering components degradation," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 104-115.
    18. Jiaqi Zhang & Li He & Hongwei Lu & Jing Li, 2014. "Importance Analysis of Groundwater Remediation Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(1), pages 115-129, January.
    19. Zhu, Xiaoyan & Hao, Yaqian, 2021. "Component rearrangement and system replacement for a system with stochastic degradation processes," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    20. Qiu, Siqi & Sallak, Mohamed & Schön, Walter & Ming, Henry X.G., 2018. "Extended LK heuristics for the optimization of linear consecutive-k-out-of-n: F systems considering parametric uncertainty and model uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 175(C), pages 51-61.

    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:taf:uiiexx:v:49:y:2017:i:7:p:722-736. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/uiie .

    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.