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1 results

  • Preservation of multivariate stochastic orders under multivariate Poisson shock models

  • Part of
  • Tityik Wong
  • Journal:
    Journal of Applied Probability / Volume 34 / Issue 4 / December 1997
    Published online by Cambridge University Press:
    14 July 2016, pp. 1009-1020
    Print publication:
    December 1997

  • Consider two systems, labeled system 1 and system 2, each with m components. Suppose component i in system k, k = 1, 2, is subjected to a sequence of shocks occurring randomly in time according to a non-explosive counting process {Γ i(t), t > 0}, i = 1, ···, m. Assume that Γ1, · ··, Γm are independent of Mk = (Mk,1, · ··, Mk,m), the number of shocks each component in system k can sustain without failure. Let Zk,i be the lifetime of component i in system k. We find conditions on processes Γ1, · ··, Tm such that some stochastic orders between M1 and M2 are transformed into some stochastic orders between Z1 and Z2. Most results are obtained under the assumption that Γ1, · ··, Γm are independent Poisson processes, but some generalizations are possible and can be seen from the proofs of theorems.