You may rely on the reliability polynomial for much more than you might think

Jack Graver, Milton Sobel

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

The reliability polynomial Rφ(p) of a collection φ of subsets of a finite set X has been extensively studied in the context of network theory. There, X is the edge set of a graph (V, X) and φ the collection of the edge sets of certain subgraphs. For example, we may take φ to be the collection of edge sets of spanning trees. In that case, Rφ(p) is the probability that, when each edge is included with the probability p, the resulting subgraph is connected. The second author defined Rφ(p) in an entirely different way enabling one to glean additional information about the collection φ from Rφ(p). Illustrating the extended information available in the reliability polynomial is the main focus of this article while demonstrating the equivalence of these two definitions is the main theoretical result.

Original languageEnglish (US)
Pages (from-to)1411-1422
Number of pages12
JournalCommunications in Statistics - Theory and Methods
Volume34
Issue number6 SPEC. ISS.
DOIs
StatePublished - Jul 4 2005

Keywords

  • Inclusion-exclusion
  • Reliability polynomial

ASJC Scopus subject areas

  • Statistics and Probability

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