IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v192y2019ics0951832017306397.html

A new cumulative shock model with damage and inter-arrival time dependency

Author

Listed:
  • Ranjkesh, Somayeh Hamed
  • Hamadani, Ali Zeinal
  • Mahmoodi, Safieh

Abstract

In this paper, a system is considered that fails when the cumulative damage due to shocks exceeds the handling capacity of the system. It is also supposed that if the time between two consecutive shocks is not large enough, the system lacks the time necessary for recovering to receive subsequent shocks; hence, larger damages might be inflicted upon the system. In other words, shocks occurring at short intervals are more fatal and cause larger damages to the system. Based on these assumptions, a new model is developed for evaluating system reliability that takes into account the likely dependencies between inter-arrival times and random shock magnitudes. The proposed model is then validated through a method based on phase-type distributions that enables the model to be efficiently and easily evaluated. Approximation of its reliability function and estimation of model parameters are also investigated. Finally, an illustrative example is provided to demonstrate the efficiency of the proposed model.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:reensy:v:192:y:2019:i:c:s0951832017306397
    DOI: 10.1016/j.ress.2018.01.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832017306397
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2018.01.006?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Marcel F. Neuts & Manish C. Bhattacharjee, 1981. "Shock models with phase type survival and shock resistance," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(2), pages 213-219, June.
    2. Gut, Allan & Hüsler, Jürg, 2005. "Realistic variation of shock models," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 187-204, September.
    Full references (including those not matched with items on IDEAS)

    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. Delia Montoro-Cazorla & Rafael Pérez-Ocón, 2022. "Analysis of k-Out-of-N-Systems with Different Units under Simultaneous Failures: A Matrix-Analytic Approach," Mathematics, MDPI, vol. 10(11), pages 1-13, June.
    2. Gregory Levitin & Maxim Finkelstein, 2018. "Optimal Mission Abort Policy for Systems Operating in a Random Environment," Risk Analysis, John Wiley & Sons, vol. 38(4), pages 795-803, April.
    3. 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).
    4. Finkelstein, Maxim & Marais, Francois, 2010. "On terminating Poisson processes in some shock models," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 874-879.
    5. Dheeraj Goyal & Nil Kamal Hazra & Maxim Finkelstein, 2022. "On Properties of the Phase-type Mixed Poisson Process and its Applications to Reliability Shock Modeling," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2933-2960, December.
    6. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2018. "Constructing a Markov process for modelling a reliability system under multiple failures and replacements," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 34-47.
    7. 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.
    8. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2018. "Mission abort policy balancing the uncompleted mission penalty and system loss risk," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 194-201.
    9. Cirillo, Pasquale & Hüsler, Jürg, 2009. "An urn approach to generalized extreme shock models," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 969-976, April.
    10. 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.
    11. Cirillo, Pasquale & Hüsler, Jürg, 2011. "Extreme shock models: An alternative perspective," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 25-30, January.
    12. Cao, Shihao & Wang, Zhihua & Liu, Chengrui & Wu, Qiong & Li, Junxing & Ouyang, Xiangmin, 2023. "A novel solution for comprehensive competing failure process considering two-phase degradation and non-Poisson shock," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    13. Levitin, Gregory & Finkelstein, Maxim & Huang, Hong-Zong, 2020. "Optimal mission abort policies for multistate systems," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    14. Levitin, Gregory & Finkelstein, Maxim, 2019. "Optimal loading of elements in series systems exposed to external shocks," Reliability Engineering and System Safety, Elsevier, vol. 192(C).
    15. Miaomiao Yu & Yinghui Tang, 2024. "Analyze periodic inspection and replacement policy of a shock and wear model with phase-type inter-shock arrival times using roots method," Journal of Risk and Reliability, , vol. 238(2), pages 233-246, April.
    16. Levitin, Gregory & Finkelstein, Maxim & Dai, Yuanshun, 2020. "Mission abort and rescue for multistate systems operating under the Poisson process of shocks," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    17. Eryilmaz, Serkan, 2015. "Assessment of a multi-state system under a shock model," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 1-8.
    18. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2014. "Matrix stochastic analysis of the maintainability of a machine under shocks," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 11-17.
    19. Montoro-Cazorla, Delia & Pérez-Ocón, Rafael, 2016. "A warmstandby system under shocks and repair governed by MAPs," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 331-338.
    20. Dheeraj Goyal & Nil Kamal Hazra & Maxim Finkelstein, 2023. "A general class of shock models with dependent inter-arrival times," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(3), pages 1079-1105, September.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    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:eee:reensy:v:192:y:2019:i:c:s0951832017306397. 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.