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Representations of component importance for coherent systems with exchangeable components
Published online by Cambridge University Press: 16 July 2020
Abstract
Two definitions of Birnbaum’s importance measure for coherent systems are studied in the case of exchangeable components. Representations of these measures in terms of distribution functions of the ordered component lifetimes are given. As an example, coherent systems with failure-dependent component lifetimes based on the notion of sequential order statistics are considered. Furthermore, it is shown that the two measures are ordered in the case of associated component lifetimes. Finally, the limiting behavior of the measures with respect to time is examined.
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- © Applied Probability Trust 2020
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