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1 results

  • A general shock model for a reliability system

  • Part of
  • Georgios Skoulakis
  • Journal:
    Journal of Applied Probability / Volume 37 / Issue 4 / December 2000
    Published online by Cambridge University Press:
    14 July 2016, pp. 925-935
    Print publication:
    December 2000

  • We study a reliability system subject to shocks generated by a renewal point process. When a shock occurs, components fail independently of each other with equal probabilities that are random numbers drawn from a distribution that may differ from shock to shock. We first consider the case of a parallel system and derive closed expressions for the Laplace-Stieltjes transform and the expectation of the time to system failure and for its density in the case that the distribution function of the renewal process possesses a density. We then treat a more general system structure, which has some very important special cases, such as k-out-of-n:F systems, and derive analogous formulae.