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Numerical comparisons of approximations of geometric sums

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  • Jean‐Louis Bon
  • Anne Philippe

Abstract

The knowledge of the failure probability of industrial systems is now a crucial test of quality. But in practice, when components are repairable, two difficulties make actually untractable the explicit calculation. The first is the number of components and the second the general distribution of the lifetime or repairtime components. Even in the Markov case, the formulae are not convenient. Nevertheless, reliability engineers use simple exponential approximations with success. This can be explained by the decomposition in a geometric sum of the system lifetime and the closeness between geometric sum and exponential. Here we resume the available approximations and give numerical comparisons. Copyright © 2004 John Wiley & Sons, Ltd.

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  • Jean‐Louis Bon & Anne Philippe, 2004. "Numerical comparisons of approximations of geometric sums," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 20(1), pages 37-48, January.
    • Handle: RePEc:wly:apsmbi:v:20:y:2004:i:1:p:37-48
    DOI: 10.1002/asmb.513
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    Cited by:

    1. Mercier, Sophie, 2007. "Discrete random bounds for general random variables and applications to reliability," European Journal of Operational Research, Elsevier, vol. 177(1), pages 378-405, February.

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