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The lifetime of a random set

Part of: Operations research and management science Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Peter C. Kiessler  and
Kanoktip Nimitkiatklai
Peter C. Kiessler*
Affiliation:
Clemson University
Kanoktip Nimitkiatklai*
Affiliation:
Clemson University
*
∗Postal address: Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA.
∗Postal address: Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA.
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Abstract

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We consider the lifetimes of systems that can be modeled as particles that move within a bounded region in ℝn. Particles move within the set according to a random walk, and particles that leave the set are lost. We divide the set into equal cells and define the lifetime of the set as the time required for the number of particles in one of the cells to fall below a predetermined threshold. We show that the lifetime of the system, given a sufficiently large number of particles, is Weibull distributed.

Keywords

Weibull distributionextreme value theoryinteracting particle system

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 2 , June 2005 , pp. 566 - 580
Copyright
© Applied Probability Trust 2005 

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