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Assessing the Reliability Function of Nanocomponents

Part of: Operations research and management science Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Nader Ebrahimi
Nader Ebrahimi*
Affiliation:
Northern Illinois University
*
∗Postal address: Division of Statistics, Northern Illinois University, DeKalb, IL 60115, USA. Email address: [email protected]
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Abstract

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A nanocomponent is a collection of atoms arranged to a specific design in order to achieve a desired function with an acceptable performance and reliability. The type of atoms, the manner in which they are arranged within the nanocomponent, and their interrelationship have a direct effect on the nanocomponent's reliability (survival) function. In this paper we propose models based on the notion of a copula that are used to describe the relationship between the atoms of a nanocomponent. Having defined these models, we go on to construct a ‘nanocomponent’ model in order to obtain the reliability function of a nanocomponent.

Keywords

Copula functionFarlie-Gumbel-Morgenstern copulaGaussian copulaisotropic covariance functionMarkov random fieldmultivariate hazard gradientreliability functionsurvival function

MSC classification

Secondary: 60G55: Point processes 90B25: Reliability, availability, maintenance, inspection
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 1 , March 2011 , pp. 31 - 42
Copyright
Copyright © Applied Probability Trust 2011 

References

Besag, J. (1974). Spatial interaction and statistical analysis of lattice systems. J. R. Statist. Soc. B 36, 192–236.Google Scholar
Ebrahimi, N. (2008). Assessing a linear nanosystem's limiting reliability from its components. J. Appl. Prob. 45, 879–887.Google Scholar
Ebrahimi, N. (2010). Assessing 2-dimensional nanocomponent's reliability. IEEE Trans. Reliab. 59, 139–144.Google Scholar
Frees, E. W. and Valdez, E. A. (2008). Hierarchical insurance claims modeling. J. Amer. Statist. Assoc. 103, 1457–1469.Google Scholar
Galambos, J. (1978). The Asymptotic Theory of Extreme Order Statistics. John Wiley, New York.Google Scholar
Johnson, N. L. and Kotz, S. (1975). A vector multivariate hazard rate. J. Multivariate Anal. 5, 53–66.Google Scholar
Johnson, R. A. and Wichern, D. W. (2007). Applied Multivariate Statistical Analysis, 6th edn. Pearson Prentice Hall, Upper Saddle River, NJ.Google Scholar
Nelson, R. B. (2006). An Introduction to Copulas, 2nd edn. Springer, New York.Google Scholar
Schabenberger, O. and Gotway, C. A. (2005). Statistical Methods for Spatial Data Analysis. Chapman and Hall/CRC, Boca Raton, FL.Google Scholar
Sklar, A. (1959). Function de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8, 229–231.Google Scholar
Slepian, D. (1962). The one-sided barrier problem for Gaussian noise. Bell System Tech. J. 41, 463–501.Google Scholar
Tong, Y. L. (1990). The Multivariate Normal Distribution. Springer, New York.Google Scholar
Yan, J. (2007). Enjoying the Joy of copulas: with a package copula. J. Statist. Software 21, 1–21.CrossRefGoogle Scholar