Some Alternate Characterizations of Reliability Domination

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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1990
Accession Number
ADA264594

Entities

People

  • A. Satyanarayana
  • C. L. Suffel
  • F. T. Boesch

Organizations

  • Stevens Institute of Technology

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DTIC Thesaurus Topics

  • Abstracts
  • Classification
  • Computations
  • Graph Theory
  • Mathematics
  • Military Research
  • New Jersey
  • Operations Research
  • Orientation (Direction)
  • Polynomials
  • Reliability
  • Security
  • Standards
  • Systems Engineering
  • Terminals

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  • Graph Algorithms and Convex Optimization.
  • Software Engineering