Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-13T00:41:33.675Z Has data issue: false hasContentIssue false
  • English
  • Français

Assessing a Linear Nanosystem's Limiting Reliability from its Components

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]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Nanosystems are devices that are in the size range of a billionth of a meter (1 x 10-9) and therefore are built necessarily from individual atoms. The one-dimensional nanosystems or linear nanosystems cover all the nanosized systems which possess one dimension that exceeds the other two dimensions, i.e. extension over one dimension is predominant over the other two dimensions. Here only two of the dimensions have to be on the nanoscale (less than 100 nanometers). In this paper we consider the structural relationship between a linear nanosystem and its atoms acting as components of the nanosystem. Using such information, we then assess the nanosystem's limiting reliability which is, of course, probabilistic in nature. We consider the linear nanosystem at a fixed moment of time, say the present moment, and we assume that the present state of the linear nanosystem depends only on the present states of its atoms.

Keywords

Binomial distributionlinear nanosystemreliabilityassociated random variables

MSC classification

Secondary: 60G55: Point processes 90B25: Reliability, availability, maintenance, inspection
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 3 , September 2008 , pp. 879 - 887
Copyright
Copyright © Applied Probability Trust 2008 

References

Bahar, R. I., Tahoori, M. B., Shukla, S. and Lombardi, F. (2005). Special Issue on ‘Challenges for Reliable design at Nanoscale’. IEEE Design and Test, July–August 2005.Google Scholar
Banerjee, S., Carlin, B. and Gelfand, A. E. (2004). Hierarchical Modeling and Analysis for Spatial Data. Chapman and Hall, New York.Google Scholar
Barlow, E. and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing: Probability Models. To begin with, Silver Spring, MD.Google Scholar
Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems. J. R. Statist. Soc. Ser. B 36, 192–236.Google Scholar
Bhushan, B. (2007). Springer Handbook of Nano-Technology, 2nd edn. Springer, Berlin.Google Scholar
Casella, G. and George, E. I. (1992). Explaining the Gibbs sampler. Amer. Statist. Assoc. 46, 167–174.Google Scholar
Drexler, K. E. (1992). Nanosystems: Molecular, Machinery, Manufacturing and Computation. John Wiley, New York.Google Scholar
Ebrahimi, N. (1990). Binary structure functions with dependent components. Adv. Appl. Prob. 22, 627–640.Google Scholar
Natvig, B. (2007). Multistate reliability theory. In Encyclopedia in Quality and Reliability, eds Ruggeri, F. et al., John Wiley, New York, pp. 1002–1010.Google Scholar
Poole, C. P. and Owens, F. J. (2003). Introduction to Nanotechnology. John Wiley, New York.Google Scholar
Ratner, M. and Ratner, D. (2003). Nanotechnology: A Gentle Introduction to the Big Idea. Prentice Hall, Englewood Cliffs, NJ.Google Scholar
Saunders, R., Kryscio, R. and Funk, G. (1979). Limiting results for arrays of binary random variables on rectangular lattices under sparseness conditions. J. Appl. Prob. 16, 554–566.CrossRefGoogle Scholar
Tabata, O. and Tsuchiya, T. (2008). Reliability of MEMS. John Wiley, New York.Google Scholar