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The number of critical connection vectors of L-superadditive structure functions

Published online by Cambridge University Press:  01 July 2016

Emad El-Neweihi  and
Fan C. Meng
Emad El-Neweihi*
Affiliation:
University of Illinois at Chicago
Fan C. Meng*
Affiliation:
University of Illinois at Chicago
*
Postal address for both authors: Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60680, USA.
Postal address for both authors: Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60680, USA.
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Abstract

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A conjecture due to Block et al. (1989), concerning the number of critical connection vectors to the various performance levels of a discrete L-superadditive structure function, is proved. When the components of the discrete L-superadditive structure function are further assumed to satisfy a certain relevance condition due to Griffith (1980), it is shown that there is exactly one critical connection vector to each performance level.

Keywords

LEVELS OF PERFORMANCECARDINALITY
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 21 , Issue 4 , December 1989 , pp. 930 - 932
Copyright
Copyright © Applied Probability Trust 1989 

Footnotes

∗

Research supported by AFOSR Grants 85-0320 and 89-0221.

∗∗

Research supported in part by AFOSR Grants 85-0320 and 89-0221.

References

Block, H. W., Griffith, W. S. and Savits, T. H. (1989) L-superadditive structure functions. Adv. Appl. Prob. 21, 919–929.Google Scholar
El-Neweihi, E. and Proschan, F. (1984) A survey of multistate system theory. Comm. Statist. A. Theory Methods 13, 405–432.Google Scholar
Griffith, W. S. (1980) Multistate reliability models. J. Appl. Prob. 17, 735–744.Google Scholar