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A dynamic stress–strength model with stochastically decreasing strength

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  • 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
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    References listed on IDEAS

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    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, September.
    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.
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    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.

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