IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v188y2019icp36-46.html
   My bibliography  Save this article

A lower bound of reliability calculating method for lattice system with non-homogeneous components

Author

Listed:
  • Lin, Cong
  • Zeng, Zhaoyang
  • Zhou, Yan
  • Xu, Ming
  • Ren, Zhanyong

Abstract

The lattice system in which the components are regularly distributed in a two dimensional area are studied due to the fact that it can be used to describe the system model in various applications, e.g., safety monitoring system, phased array radar, design of array antenna or liquid crystal display. In the previous research, the common shared assumption is that the lattice system is composed with homogeneous components. However, when we conduct a reliability evaluation of the system, this hypothesis is easy to be violated, because maintenance action may take upon to replace the aging components with new ones, which leads the residual life of the components are different from each other. In this paper we employ finite Markov chain imbedding approach and use the “k-within-r × s-out-of-m × n†model to obtain a lower bound calculating method for reliability of the lattice system with non-homogeneous components. By changing parameters or adding conditions, we propose some transformed models from the original one. Some numerical examples are applied to illustrate how to compute the reliability of these models and address some property of the lattice system.

Suggested Citation

  • Lin, Cong & Zeng, Zhaoyang & Zhou, Yan & Xu, Ming & Ren, Zhanyong, 2019. "A lower bound of reliability calculating method for lattice system with non-homogeneous components," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 36-46.
    • Handle: RePEc:eee:reensy:v:188:y:2019:i:c:p:36-46
    DOI: 10.1016/j.ress.2019.03.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832018311943
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2019.03.009?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. Eryilmaz, Serkan, 2018. "The number of failed components in a k-out-of-n system consisting of multiple types of components," Reliability Engineering and System Safety, Elsevier, vol. 175(C), pages 246-250.
    2. James Fu & Markos Koutras, 1994. "Poisson approximations for 2-dimensional patterns," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 179-192, March.
    3. Shijia Du & Cong Lin & Lirong Cui, 2016. "Reliabilities of a single-unit system with multi-phased missions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(9), pages 2524-2537, May.
    4. Anant P. Godbole & Laura K. Potter & Jessica K. Sklar, 1998. "Improved upper bounds for the reliability of d‐dimensional consecutive‐k‐out‐of‐n : F systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(2), pages 219-230, March.
    5. Wan-Chen Lee, 2015. "Power of Discrete Scan Statistics: a Finite Markov Chain Imbedding Approach," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 833-841, September.
    6. 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.
    7. Zhao, Xian & Wang, Siqi & Wang, Xiaoyue & Cai, Kui, 2018. "A multi-state shock model with mutative failure patterns," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 1-11.
    8. Tomoaki Akiba & Hisashi Yamamoto, 2001. "Reliability of a 2‐dimensional k‐within‐consecutive‐r × s‐out‐of‐m × n:F system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(7), pages 625-637, October.
    9. Zhao, Xian & Wang, Xiaoyue & Sun, Ge, 2015. "Start-up demonstration tests with sparse connection," European Journal of Operational Research, Elsevier, vol. 243(3), pages 865-873.
    10. Yung-Ming Chang & Tung-Lung Wu, 2011. "On Average Run Lengths of Control Charts for Autocorrelated Processes," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 419-431, June.
    11. 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.
    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. Taishin Nakamura & Hisashi Yamamoto & Tomoaki Akiba, 2022. "Reliability of a toroidal connected-(r,s)-out-of-(m,n):F lattice system," Journal of Risk and Reliability, , vol. 236(2), pages 329-338, April.
    2. Yi, He & Balakrishnan, Narayanaswamy & Li, Xiang, 2023. "Reliability of three-dimensional consecutive k-type systems," Reliability Engineering and System Safety, Elsevier, vol. 233(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. 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).
    2. Yaguang Wu & Qingan Qiu, 2022. "Optimal Triggering Policy of Protective Devices Considering Self-Exciting Mechanism of Shocks," Mathematics, MDPI, vol. 10(15), pages 1-18, August.
    3. Hisashi Yamamoto & Tomoaki Akiba, 2005. "Evaluating methods for the reliability of a large 2‐dimensional rectangular k‐within‐consecutive‐(r, s)‐out‐of‐(m, n):F system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(3), pages 243-252, April.
    4. Yin, Juan & Cui, Lirong & Balakrishnan, Narayanaswamy, 2022. "Reliability of consecutive-(k,l)-out-of-n: F systems with shared components under non-homogeneous Markov dependence," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    5. Xian Zhao & Jing Zhang & Xiaoyue Wang, 2019. "Joint optimization of components redundancy, spares inventory and repairmen allocation for a standby series system," Journal of Risk and Reliability, , vol. 233(4), pages 623-638, August.
    6. Jingwen Lu & He Yi & Xiang Li & Narayanaswamy Balakrishnan, 2023. "Joint Reliability of Two Consecutive-(1, l) or (2, k)-out-of-(2, n): F Type Systems and Its Application in Smart Street Light Deployment," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    7. Eryilmaz, Serkan & Devrim, Yilser, 2019. "Reliability and optimal replacement policy for a k-out-of-n system subject to shocks," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 393-397.
    8. Wang, Jingjing & Zhao, Xian & Guo, Xiaoxin, 2019. "Optimizing wind turbine's maintenance policies under performance-based contract," Renewable Energy, Elsevier, vol. 135(C), pages 626-634.
    9. Zhao, Xian & Lv, Zuheng & Qiu, Qingan & Wu, Yaguang, 2023. "Designing two-level rescue depot location and dynamic rescue policies for unmanned vehicles," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    10. 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).
    11. Qinglai Dong & Lirong Cui & Hongda Gao, 2019. "A bivariate replacement policy for an imperfect repair system based on geometric processes," Journal of Risk and Reliability, , vol. 233(4), pages 670-681, August.
    12. Xian Zhao & Xinqian Huang & Jinglei Sun, 2020. "Reliability modeling and maintenance optimization for the two-unit system with preset self-repairing mechanism," Journal of Risk and Reliability, , vol. 234(2), pages 221-234, April.
    13. 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.
    14. 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.
    15. Zhao, Xian & Wang, Siqi & Wang, Xiaoyue & Fan, Yu, 2020. "Multi-state balanced systems in a shock environment," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    16. Zhao, Xian & Li, Rong & Cao, Shuai & Qiu, Qingan, 2023. "Joint modeling of loading and mission abort policies for systems operating in dynamic environments," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    17. Qiu, Qingan & Kou, Meng & Chen, Ke & Deng, Qiao & Kang, Fengming & Lin, Cong, 2021. "Optimal stopping problems for mission oriented systems considering time redundancy," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    18. Xiaofei Chai & Boyu Chen & Xian Zhao, 2023. "Optimal Mission Abort Decisions for Multi-Component Systems Considering Multiple Abort Criteria," Mathematics, MDPI, vol. 11(24), pages 1-12, December.
    19. 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.
    20. 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).

    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:188:y:2019:i:c:p:36-46. 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.