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Representations of component importance for coherent systems with exchangeable components

Published online by Cambridge University Press:  16 July 2020

S. Pitzen*
Affiliation:
RWTH Aachen University
M. Burkschat*
Affiliation:
RWTH Aachen University
*
*Postal address: Institute of Statistics, RWTH Aachen University, D-52056 Aachen, Germany.
*Postal address: Institute of Statistics, RWTH Aachen University, D-52056 Aachen, Germany.

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.

Type
Research Papers
Copyright
© Applied Probability Trust 2020

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