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Some Alternate Characterizations of Reliability Domination

Published online by Cambridge University Press:  27 July 2009

F. T. Boesch ,
A. Satyanarayana  and
C. L. Suffel
F. T. Boesch
Affiliation:
Stevens Institute of Technology Hoboken, New Jersey 07030
A. Satyanarayana
Affiliation:
Stevens Institute of Technology Hoboken, New Jersey 07030
C. L. Suffel
Affiliation:
Stevens Institute of Technology Hoboken, New Jersey 07030
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Abstract

An important problem in reliability theory is to determine the reliability of a system from the reliability of its components. If E is a finite set of components, then certain subsets of E are prescribed to be the operating states of the system. A formation is any collection F of minimal operating states whose union is E. Reliability domination is defined as the total number of odd cardinality formations minus the total number of even cardinality formations. The purpose of this paper is to establish some new results concerning reliability domination. In the special case where the system can be identified with a graph or digraph, these new results lead to some new graph-theoretic properties and to simple proofs of certain known theorems. The pertinent graph-theoretic properties include spanning trees, acyclic orientations, Whitney's broken cycles, and Tutte's internal activity associated with the chromatic polynomial.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 4 , Issue 2 , April 1990 , pp. 257 - 276
Copyright
Copyright © Cambridge University Press 1990

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