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1 results

  • Shock models by underlying counting process

  • Part of
  • Franco Pellerey
  • Journal:
    Journal of Applied Probability / Volume 31 / Issue 1 / March 1994
    Published online by Cambridge University Press:
    14 July 2016, pp. 156-166
    Print publication:
    March 1994

  • Suppose that a device is subjected to shocks governed by a counting process N = {N(t), t ≧0}. The probability that the device survives beyond time t is then H̄(t)=Σk=0∞Q̄ℙ[N(t)=k], where Q̄k is the probability of surviving k shocks. It is known that H is NBU if the interarrivals Uk, ∊ ℕ+, are independent and NBU, and Q̄k+j ≦ Q̄k· Q̄j holds whenever k, j ∊ ℕ. Similar results hold for the classes of the NBUE and HNBUE distributions. We show that some other ageing classes have similar properties.