IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v166y2017icp99-108.html
   My bibliography  Save this article

On sensitivity analysis of aging multi-state system by using LZ-transform

Author

Listed:
  • Lisnianski, Anatoly
  • Frenkel, Ilia
  • Khvatskin, Lev

Abstract

The paper considers a sensitivity evaluation for an aging multi-state system (MSS) under minimal repair. Investigation of an impact of changing different failure/repair rates of different elements in MSS is important for practical reliability engineering. In practical reliability engineering a "curse of dimensionality" (the large number of states that should be analyzed for a multi-state system model) is a main obstacle for sensitivity assessment. Straightforward Markov Method applied to solve this problem requires building a model with numerous numbers of states and solving a corresponding system of differential equations. In order to solve this problem, the paper proposes to use a new method based on an LZ-transform of the discrete-state continuous-time Markov process, and on Ushakov's Universal Generating Operator. New sensitivity measures useful for aging MSS reliability analysis were introduced. It was shown that the proposed method drastically reduces a computational burden. A numerical example is presented in order to illustrate the approach.

Suggested Citation

  • Lisnianski, Anatoly & Frenkel, Ilia & Khvatskin, Lev, 2017. "On sensitivity analysis of aging multi-state system by using LZ-transform," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 99-108.
    • Handle: RePEc:eee:reensy:v:166:y:2017:i:c:p:99-108
    DOI: 10.1016/j.ress.2016.12.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832016309334
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2016.12.001?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. Peng, Rui & Zhai, Qingqing & Xing, Liudong & Yang, Jun, 2014. "Reliability of demand-based phased-mission systems subject to fault level coverage," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 18-25.
    2. Natvig, Bent, 1979. "A suggestion of a new measure of importance of system components," Stochastic Processes and their Applications, Elsevier, vol. 9(3), pages 319-330, December.
    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. 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.
    2. Xiao, Hui & Zhang, Yiyun & Xiang, Yisha & Peng, Rui, 2020. "Optimal design of a linear sliding window system with consideration of performance sharing," Reliability Engineering and System Safety, Elsevier, vol. 198(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. Dui, Hongyan & Si, Shubin & Wu, Shaomin & Yam, Richard C.M., 2017. "An importance measure for multistate systems with external factors," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 49-57.
    2. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Mission abort policy optimization for series systems with overlapping primary and rescue subsystems operating in a random environment," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    3. 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.
    4. Peng, Rui & Wu, Di & Xiao, Hui & Xing, Liudong & Gao, Kaiye, 2019. "Redundancy versus protection for a non-reparable phased-mission system subject to external impacts," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    5. Levitin, Gregory & Finkelstein, Maxim, 2018. "Optimal mission abort policy for systems in a random environment with variable shock rate," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 11-17.
    6. Wu, Shaomin & Coolen, Frank P.A., 2013. "A cost-based importance measure for system components: An extension of the Birnbaum importance," European Journal of Operational Research, Elsevier, vol. 225(1), pages 189-195.
    7. Navarro, Jorge & Arriaza, Antonio & Suárez-Llorens, Alfonso, 2019. "Minimal repair of failed components in coherent systems," European Journal of Operational Research, Elsevier, vol. 279(3), pages 951-964.
    8. Jia, Heping & Ding, Yi & Peng, Rui & Liu, Hanlin & Song, Yonghua, 2020. "Reliability assessment and activation sequence optimization of non-repairable multi-state generation systems considering warm standby," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    9. Huan Yu & Jun Yang & Yu Zhao, 2018. "Reliability of nonrepairable phased-mission systems with common bus performance sharing," Journal of Risk and Reliability, , vol. 232(6), pages 647-660, December.
    10. 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.
    11. Bent Natvig, 2011. "Measures of Component Importance in Nonrepairable and Repairable Multistate Strongly Coherent Systems," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 523-547, September.
    12. Li, Yan & Cui, Lirong & Lin, Cong, 2017. "Modeling and analysis for multi-state systems with discrete-time Markov regime-switching," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 41-49.
    13. Natvig, Bent & Eide, Kristina A. & Gåsemyr, Jørund & Huseby, Arne B. & Isaksen, Stefan L., 2009. "Simulation based analysis and an application to an offshore oil and gas production system of the Natvig measures of component importance in repairable systems," Reliability Engineering and System Safety, Elsevier, vol. 94(10), pages 1629-1638.
    14. Li, Ruiying & Gao, Ying, 2022. "On the component resilience importance measures for infrastructure systems," International Journal of Critical Infrastructure Protection, Elsevier, vol. 36(C).
    15. Huseby, Arne B. & Natvig, Bent, 2013. "Discrete event simulation methods applied to advanced importance measures of repairable components in multistate network flow systems," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 186-198.
    16. Ke Chen & Xian Zhao & Qingan Qiu, 2022. "Optimal Task Abort and Maintenance Policies Considering Time Redundancy," Mathematics, MDPI, vol. 10(9), pages 1-16, April.
    17. Zhu, Xiaoyan & Chen, Zhiqiang & Borgonovo, Emanuele, 2021. "Remaining-useful-lifetime and system-remaining-profit based importance measures for decisions on preventive maintenance," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    18. Zhu, Xiaoning & Yan, Rui & Peng, Rui & Zhang, Zhongxin, 2020. "Optimal routing, loading and aborting of UAVs executing both visiting tasks and transportation tasks," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    19. Wang, Chaonan & Xing, Liudong & Levitin, Gregory, 2015. "Probabilistic common cause failures in phased-mission systems," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 53-60.
    20. Gregory Levitin & Maxim Finkelstein, 2018. "Optimal mission abort policy with multiple shock number thresholds," Journal of Risk and Reliability, , vol. 232(6), pages 607-615, December.

    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:166:y:2017:i:c:p:99-108. 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.