A MULTIVARIATE NOTION OF ASSOCIATION, WITH A RELIABILITY APPLICATION
BOEING SCIENTIFIC RESEARCH LABS SEATTLE WA MATHEMATICS RESEARCH LAB
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Random variables T1,T2,...,Tn are, in this paper, associated if each pair of non-decreasing functions FT1,T2,...,Tn, GT1,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.
- Statistics and Probability
- Manufacturing and Industrial Engineering and Control of Production Systems