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1 results

  • General shock models associated with correlated renewal sequences

  • J. G. Shanthikumar, U. Sumita
  • Journal:
    Journal of Applied Probability / Volume 20 / Issue 3 / September 1983
    Published online by Cambridge University Press:
    14 July 2016, pp. 600-614
    Print publication:
    September 1983

  • In this paper we define and analyze a general shock model associated with a correlated pair (Xn, Yn) of renewal sequences, where the system fails when the magnitude of a shock exceeds (or falls below) a prespecified threshold level. Two models, depending on whether the nth shock Xn is correlated to the length Yn of the interval since the last shock, or to the length Yn of the subsequent interval until the next shock, are considered. The transform results, an exponential limit theorem, and properties of the associated renewal process of the failure times are obtained. An application in a stochastic clearing system with numerical results is also given.