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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. repec:eee:reensy:v:92:y:2007:i:12:p:1651-1658 is not listed on IDEAS
    2. 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, February.
    3. 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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