Accession Number : AD0644094

Title :   A MULTIVARIATE NOTION OF ASSOCIATION, WITH A RELIABILITY APPLICATION,

Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB

Personal Author(s) : Esary,J. D. ; Proschan,Frank ; Walkup,D. W.

Report Date : OCT 1966

Pagination or Media Count : 26

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. (Author)

Descriptors :   (*MULTIVARIATE ANALYSIS, *RANDOM VARIABLES), (*RELIABILITY, MULTIVARIATE ANALYSIS), STOCHASTIC PROCESSES, SET THEORY

Subject Categories : Statistics and Probability
      Mfg & Industrial Eng & Control of Product Sys

Distribution Statement : APPROVED FOR PUBLIC RELEASE