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Assessing a Linear Nanosystem's Limiting Reliability from its Components

Part of:Operations research and management scienceStochastic 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: nader@math.niu.edu
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Abstract

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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 processes90B25: Reliability, availability, maintenance, inspection

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 3 , September 2008, pp. 879 - 887
Copyright
Copyright © Applied Probability Trust 2008 

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