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1 results

  • Optimum replacement of a system subject to shocks

  • Mohamed Abdel-Hameed
  • Journal:
    Journal of Applied Probability / Volume 23 / Issue 1 / March 1986
    Published online by Cambridge University Press:
    14 July 2016, pp. 107-114
    Print publication:
    March 1986

  • A system is subject to shocks. Each shock weakens the system and makes it more expensive to run. It is desirable to determine a replacement time for the system. Boland and Proschan [4] consider periodic replacement of the system and give sufficient conditions for the existence of an optimal finite period, assuming that the shock process is a non-homogeneous Poisson process and the cost structure does not depend on time. Block et al. [3] establish similar results assuming that cost structure is time dependent, still requiring that the shock process is a non-homogeneous Poisson process. We show via a sample path argument that the results of [3] and [4] hold for any counting process whose jump size is of one unit magnitude.