A MULTIVARIATE NOTION OF ASSOCIATION, WITH A RELIABILITY APPLICATION

Abstract

Random variables T1,T2,...,Tn are, in this paper, associated if each pair of non-decreasing functions F(T1,T2,...,Tn), G(T1,T2,...,Tn) have a non- negative covariance. Association holds in cases ranging from T1,T2,...,Tn independent to T1,T2,...,Tn jointly restricted to a non-decreasing curve. Association is preserved under the standard multivariate operations of extracting subsets and pooling independent sets; and under the special operation of forming sets of non-decreasing functions. Suitable choices of F,G lead to various inequalities for associated random variables. The properties of association are studied in the simple, but representative, case that T1,T2,..., Tn are finitely discrete. The notion of association is useful in extending the domain of validity of the minimal cut lower bound for the reliability of a coherent system, notably (here) to the case of repairable components with exponential times to failure and exponential times to repair.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1966
Accession Number
AD0644094

Entities

People

  • D. W. Walkup
  • Frank Proschan
  • J. D. Esary

Organizations

  • Boeing

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Inequalities
  • Mathematics
  • Probability
  • Probability Distributions
  • Random Variables
  • Reliability
  • Scientific Research
  • Standards
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Neural Network Machine Learning.
  • Statistical inference.