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An Integrated Probabilistic Model for Assessing a Nanocomponent's Reliability

Part of: Stochastic processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Nader Ebrahimi  and
Yarong Yang
Nader Ebrahimi*
Affiliation:
Northern Illinois University
Yarong Yang*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Division of Statistics, Northern Illinois University, DeKalb, IL 60115, USA. Email address: nader@math.niu.edu
∗∗ Postal address: Department of Civil and Environmental Engineering, University of California, Berkeley, CA 94720, USA.
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Abstract

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We construct an integrated probabilistic model to capture interactions between atoms of a nanocomponent. We then use this model to assess reliabilities of nanocomponents with different structures. Several properties of our proposed model are also described under a sparseness condition. The model is an extension of our previous model based on Markovian random field theory. The proposed integrated model is flexible in that pairwise relationship information among atoms as well as features of individual atoms can be easily incorporated. An important feature that distinguishes the integrated probabilistic model from our previous model is that the integrated approach uses all available sources of information with different weights for different types of interaction. In this paper we consider the nanocomponent at a fixed moment of time, say the present moment, and we assume that the present state of the nanocomponent depends only on the present states of its atoms.

Keywords

Associated random variableconditionally increasing in sequenceGibbs distributionGibbs samplingMarkov random fieldreliability

MSC classification

Secondary: 60G55: Point processes 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 3 , September 2011 , pp. 832 - 842
Copyright
Copyright © Applied Probability Trust 2011 

References

Barlow, R. E. and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring, MD.Google Scholar
Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems. J. R. Statist. Soc. B {36,} 192–236.Google Scholar
Bloemena, A. R. (1964). Sampling from a Graph (Math. Centre Tracts 2). Mathematisch Centrum, Amesterdam.Google Scholar
Casella, G. and George, E. I. (1992). Explaining the Gibbs sampler. Amer. Statistician {46,} 167–174.Google Scholar
Deng, M., Chen, T. and Sun, F. (2004). An integrated probabilistic model for functional prediction of proteins. J. Comput. Biol. {11,} 463–475.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 limiting reliability. IEEE Trans. Reliab. {59,} 139–144.Google Scholar
Saunders, R., Kryscio, R. and Funk, G. M. (1979). Limiting results for arrays of binary random variables on rectangular lattices under sparseness conditions. J. Appl. Prob. {16,} 554–566.Google Scholar