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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*
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.

Type
Letters to the Editor
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, 919929.Google Scholar
El-Neweihi, E. and Proschan, F. (1984) A survey of multistate system theory. Comm. Statist. A. Theory Methods 13, 405432.Google Scholar
Griffith, W. S. (1980) Multistate reliability models. J. Appl. Prob. 17, 735744.Google Scholar