New shock models based on the generalized Polya process

Ji Hwan Cha, Maxim Finkelstein

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23 Scopus citations

Abstract

Various shock models have been extensively studied in the literature, mostly under the assumption of the Poisson process of shocks. In the current paper, we study shock models under the generalized Polya process (GPP) of shocks, which has been recently introduced and characterized in the literature (see Konno (2010) and Cha, 2014). Distinct from the widely used nonhomogeneous Poisson process, the important feature of this process is the dependence of its stochastic intensity on the number of previous shocks. We consider the extreme shock model, where each shock is catastrophic for a system with probability p(t) and is harmless with the complementary probability q(t)=1-p(t). The corresponding survival and the failure rate functions are derived and analyzed. These results can be used in various applications including engineering, survival analysis, finance, biology and so forth. The cumulative shock model, where each shock results in the increment of wear and a system's failure occurs when the accumulated wear reaches some boundary is also considered. A new general concept describing the dependent increments property of a stochastic process is suggested and discussed with respect to the GPP.

Original languageEnglish
Pages (from-to)135-141
Number of pages7
JournalEuropean Journal of Operational Research
Volume251
Issue number1
DOIs
StatePublished - 16 May 2016

Keywords

  • Combined shock model
  • Cumulative shock model
  • Extreme shock model
  • Generalized Polya process
  • Time-dependent wear

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