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Numerical comparisons of approximations of geometric sums
Author(s) -
Bon JeanLouis,
Philippe Anne
Publication year - 2004
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.513
Subject(s) - closeness , simple (philosophy) , exponential function , exponential distribution , markov chain , reliability (semiconductor) , mathematics , geometric mean , geometric distribution , decomposition , computer science , probability distribution , statistics , mathematical analysis , ecology , philosophy , power (physics) , physics , epistemology , quantum mechanics , biology
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.