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2 results

  • Hazard Rate Properties of a General Counting Process Stopped at an Independent Random Time

  • Part of
  • F. G. Badia
  • Journal:
    Journal of Applied Probability / Volume 48 / Issue 1 / March 2011
    Published online by Cambridge University Press:
    14 July 2016, pp. 56-67
    Print publication:
    March 2011
    • Article
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  • In this work we provide sufficient conditions under which a general counting process stopped at a random time independent from the process belongs to the reliability decreasing reversed hazard rate (DRHR) or increasing failure rate (IFR) class. We also give some applications of these results in generalized renewal and trend renewal processes stopped at a random time.

  • On increasing-failure-rate random variables

  • Part of
  • Sheldon M. Ross, J. George Shanthikumar, Zegang Zhu
  • Journal:
    Journal of Applied Probability / Volume 42 / Issue 3 / September 2005
    Published online by Cambridge University Press:
    14 July 2016, pp. 797-809
    Print publication:
    September 2005
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  • We provide sufficient conditions for the following types of random variable to have the increasing-failure-rate (IFR) property: sums of a random number of random variables; the time at which a Markov chain crosses a random threshold; the time until a random number of events have occurred in an inhomogeneous Poisson process; and the number of events of a renewal process, and of a general counting process, that have occurred by a randomly distributed time.