IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v78y2015i7p807-827.html
   My bibliography  Save this article

A dynamic stress–strength model with stochastically decreasing strength

Author

Listed:
  • Ji Cha
  • Maxim Finkelstein

Abstract

We consider a dynamic stress–strength model under external shocks. The strength of the system decreases with time and the failure occurs when the strength finally vanishes. Furthermore, there is another cause of the system failure induced by an external shock process. Each shock is characterized by the corresponding stress. If the magnitude of the stress exceeds the current strength, then the system also fails. We assume that the initial strength of the system and its decreasing drift pattern are random. We derive the survival function of the system and interpret the time-dependent dynamic changes of the random quantities which govern the reliability performance of the system. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Ji Cha & Maxim Finkelstein, 2015. "A dynamic stress–strength model with stochastically decreasing strength," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 807-827, October.
    • Handle: RePEc:spr:metrik:v:78:y:2015:i:7:p:807-827
    DOI: 10.1007/s00184-015-0528-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00184-015-0528-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00184-015-0528-x?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. van Noortwijk, J.M., 2009. "A survey of the application of gamma processes in maintenance," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 2-21.
    2. van Noortwijk, J.M. & van der Weide, J.A.M. & Kallen, M.J. & Pandey, M.D., 2007. "Gamma processes and peaks-over-threshold distributions for time-dependent reliability," Reliability Engineering and System Safety, Elsevier, vol. 92(12), pages 1651-1658.
    3. Ting Li & James Anderson, 2013. "Shaping human mortality patterns through intrinsic and extrinsic vitality processes," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 28(12), pages 341-372.
    4. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, February.
    5. Maxim Finkelstein & Ji Hwan Cha, 2013. "Shocks as Burn-in," Springer Series in Reliability Engineering, in: Stochastic Modeling for Reliability, edition 127, chapter 0, pages 313-361, Springer.
    6. Savits, Thomas H. & Shaked, Moshe, 1981. "Shock models and the MIFRA property," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 273-283, August.
    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. Ye, Kewei & Wang, Han & Ma, Xiaobing, 2023. "A generalized dynamic stress-strength interference model under δ-failure criterion for self-healing protective structure," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    2. Hyunju Lee & Ji Hwan Cha, 2021. "A general multivariate new better than used (MNBU) distribution and its properties," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(1), pages 27-46, January.

    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. Finkelstein, Maxim & Ludick, Zani, 2014. "On some steady-state characteristics of systems with gradual repair," Reliability Engineering and System Safety, Elsevier, vol. 128(C), pages 17-23.
    2. Maxim Finkelstein & Ji Hwan Cha, 2022. "Reducing degradation and age of items in imperfect repair modeling," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1058-1081, December.
    3. Cha, Ji Hwan & Pulcini, Gianpaolo, 2016. "Optimal burn-in procedure for mixed populations based on the device degradation process history," European Journal of Operational Research, Elsevier, vol. 251(3), pages 988-998.
    4. Maxim Finkelstein & Ji Hwan Cha, 2021. "On degradation-based imperfect repair and induced generalized renewal processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 1026-1045, December.
    5. Shafiee, Mahmood & Finkelstein, Maxim & Bérenguer, Christophe, 2015. "An opportunistic condition-based maintenance policy for offshore wind turbine blades subjected to degradation and environmental shocks," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 463-471.
    6. Finkelstein, Maxim, 2013. "On some comparisons of lifetimes for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 300-304.
    7. Mahmood Shafiee & Maxim Finkelstein, 2015. "A proactive group maintenance policy for continuously monitored deteriorating systems: Application to offshore wind turbines," Journal of Risk and Reliability, , vol. 229(5), pages 373-384, October.
    8. Caballé, N.C. & Castro, I.T. & Pérez, C.J. & Lanza-Gutiérrez, J.M., 2015. "A condition-based maintenance of a dependent degradation-threshold-shock model in a system with multiple degradation processes," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 98-109.
    9. Shafiee, Mahmood & Finkelstein, Maxim, 2015. "An optimal age-based group maintenance policy for multi-unit degrading systems," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 230-238.
    10. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "Justifying the Gompertz curve of mortality via the generalized Polya process of shocks," Theoretical Population Biology, Elsevier, vol. 109(C), pages 54-62.
    11. 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).
    12. Ji Hwan Cha & Maxim Finkelstein, 2020. "On optimal life extension for degrading systems," Journal of Risk and Reliability, , vol. 234(3), pages 487-495, June.
    13. 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.
    14. 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.
    15. Wang, Changxi & Elsayed, Elsayed A., 2020. "Stochastic modeling of corrosion growth," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    16. Cha, Ji Hwan & Finkelstein, Maxim, 2019. "Stochastic modeling for systems with delayed failures," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 118-124.
    17. Huynh, K.T. & Barros, A. & Bérenguer, C. & Castro, I.T., 2011. "A periodic inspection and replacement policy for systems subject to competing failure modes due to degradation and traumatic events," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 497-508.
    18. 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.
    19. Ji Hwan Cha & Maxim Finkelstein, 2019. "Optimal preventive maintenance for systems having a continuous output and operating in a random environment," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 327-350, July.
    20. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "New shock models based on the generalized Polya process," European Journal of Operational Research, Elsevier, vol. 251(1), pages 135-141.

    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:spr:metrik:v:78:y:2015:i:7:p:807-827. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.