On Bounds for the Monotone-Structure Reliability

On Bounds for the Monotone-Structure Reliability At present, two types of attainable bounds on the reliability of a general monotone structure are known. Packing bounds are trivial. Untying bounds were obtained by Polesskii in 1997. Their special case, the classical Esary–Proschan bounds, are known since 1963. In the present paper, we introduce the third type of attainable bounds on the reliability of a general monotone structure. We call them difference-untying bounds. They are generalization and improvement of the Oxley–Welsh bounds on the reliability of a homogeneous monotone structure obtained in 1979. An example demonstrating the high quality of difference-untying bounds is given. As a consequence, we obtain new bounds on the number of members of an arbitrary simplicial complex. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

On Bounds for the Monotone-Structure Reliability

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Publisher
Springer Journals
Copyright
Copyright © 2001 by MAIK “Nauka/Interperiodica”
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1023/A:1013831619318
Publisher site
See Article on Publisher Site

Abstract

At present, two types of attainable bounds on the reliability of a general monotone structure are known. Packing bounds are trivial. Untying bounds were obtained by Polesskii in 1997. Their special case, the classical Esary–Proschan bounds, are known since 1963. In the present paper, we introduce the third type of attainable bounds on the reliability of a general monotone structure. We call them difference-untying bounds. They are generalization and improvement of the Oxley–Welsh bounds on the reliability of a homogeneous monotone structure obtained in 1979. An example demonstrating the high quality of difference-untying bounds is given. As a consequence, we obtain new bounds on the number of members of an arbitrary simplicial complex.

Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 9, 2004

References

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