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Bounding the stochastic performance of continuum structure functions. I

Published online by Cambridge University Press:  14 July 2016

Laurence A. Baxter  and
Chul Kim
Laurence A. Baxter*
Affiliation:
State University of New York at Stony Brook
Chul Kim
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.
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Abstract

A continuum structure function γ is a non-decreasing mapping from the unit hypercube to the unit interval. Minimal path (cut) sets of upper (lower) simple continuum structure functions are introduced and are used to determine bounds on the distribution of γ (Χ) when X is a vector of associated random variables and when γ is right (left)-continuous. It is shown that, if γ admits of a modular decomposition, improved bounds may be obtained.

Keywords

WEAK COHERENCYMINIMAL PATH SETMINIMAL CUT SETUPPER SIMPLELOWER SIMPLEMODULEMODULAR DECOMPOSITIONASSOCIATED RANDOM VARIABLE
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 660 - 669
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

∗∗

Present address: Agency for Defense Development, P.O. Box 35, Daejeon, Korea.

Research supported by the National Science Foundation under grant ECS-8306871 and, in part, by the Air Force Office of Scientific Research, AFSC, USAF under grant AFOSR-84-0243. The US Government is authorised to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.

References

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Baxter, L. A. and Kim, C. (1986) Modules of continuum structures. In Reliability and Quality Control, ed. Basu, A. P., North-Holland, Amsterdam, 57–68.Google Scholar
Block, H. W. and Savits, T. H. (1984) Continuous multistate structure functions. Operat. Res. 32, 703–714.CrossRefGoogle Scholar