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Structure functions with finite minimal vector sets

Published online by Cambridge University Press:  14 July 2016

Laurence A. Baxter  and
Seung Min Lee
Laurence A. Baxter*
Affiliation:
State University of New York at Stony Brook
Seung Min Lee*
Affiliation:
State University of New York at Stony Brook
*
∗Postal address: Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, NY 11794, USA.
∗∗Present address: Department of Statistics, Hallym University, 1 Okchon-dong, Chunchon 200, Korea.
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Abstract

A continuum structure function (CSF) y is a non-decreasing mapping from the unit hypercube to the unit interval. Define whereas γ (γ) < α for all y < x}, the set of minimal vectors to level α. This paper examines CSFs for which each Pα is finite. It is shown that if γ is such a CSF and X is a vector of independent random variables, the distribution of γ (X) is readily calculated. Further, if γ is an arbitrary right-continuous CSF, the distribution of γ (X) may be approximated arbitrarily closely by that of γ′(X) where γ′ is a right-continuous CSF for which each minimal vector set is finite.

Keywords

CONTINUUM STRUCTURE FUNCTIONMINIMAL VECTOR SETREDUCTION MAPPINGSTOCHASTIC PERFORMANCE FUNCTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 26 , Issue 1 , March 1989 , pp. 196 - 201
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

Research supported by the Air Force Office of Scientific Research, AFSC, USAF under grant AFOSR-86-0136. The US Government is authorised to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.

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