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2 results

  • Ordering of repairable systems

  • Nader Ebrahimi
  • Journal:
    Journal of Applied Probability / Volume 27 / Issue 1 / March 1990
    Published online by Cambridge University Press:
    14 July 2016, pp. 193-201
    Print publication:
    March 1990

  • The problem of how to compare repairable systems has long been of interest to those who are engaged in reliability analysis. In this article we have introduced a type of comparison of two counting processes. Various properties and applications of our stochastic comparison are also studied.

  • Order statistics, Poisson processes and repairable systems

  • Douglas R. Miller
  • Journal:
    Journal of Applied Probability / Volume 13 / Issue 3 / September 1976
    Published online by Cambridge University Press:
    14 July 2016, pp. 519-529
    Print publication:
    September 1976

  • Necessary and sufficient conditions are presented under which the point processes equivalent to order statistics of n i.i.d. random variables or superpositions of n i.i.d. renewal processes converge to a non-degenerate limiting process as n approaches infinity. The limiting process must be one of three types of non-homogeneous Poisson process, one of which is the Weibull process. These point processes occur as failure-time models in the reliability theory of repairable systems.