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2 results

  • On the HNBUE property in a class of correlated cumulative shock models

  • Part of
  • Rafael Pérez-Ocón, M. Luz Gámiz-Pérez
  • Journal:
    Advances in Applied Probability / Volume 27 / Issue 4 / December 1995
    Published online by Cambridge University Press:
    01 July 2016, pp. 1186-1188
    Print publication:
    December 1995
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  • Conditions for a correlated cumulative shock model under which the system failure time is HNBUE are given. It is shown that the proof of a theorem given by Sumita and Shanthikumar (1985) relative to this property is not correct and a correct proof of the theorem is given.

  • Distribution properties of the system failure time in a general shock model

  • J. G. Shanthikumar, Ushio Sumita
  • Journal:
    Advances in Applied Probability / Volume 16 / Issue 2 / June 1984
    Published online by Cambridge University Press:
    01 July 2016, pp. 363-377
    Print publication:
    June 1984

  • In this paper we study some distribution properties of the system failure time in general shock models associated with correlated renewal sequences (Xn, Yn) . Two models, depending on whether the magnitude of the nth shock Xn is correlated to the length Yn of the interval since the last shock, or to the length of the subsequent interval to the next shock, are considered. Sufficient conditions under which the system failure time is completely monotone, new better than used, new better than used in expectation, and harmonic new better than used in expectation are given for these two models.