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Order statistics, Poisson processes and repairable systems

Published online by Cambridge University Press:  14 July 2016

Douglas R. Miller
Douglas R. Miller*
Affiliation:
University of Missouri - Columbia
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Abstract

Necessary and sufficient conditions are presented under which the point processes equivalent to order statistics of n i.i.d. random variables or superpositions of n i.i.d. renewal processes converge to a non-degenerate limiting process as n approaches infinity. The limiting process must be one of three types of non-homogeneous Poisson process, one of which is the Weibull process. These point processes occur as failure-time models in the reliability theory of repairable systems.

Keywords

ORDER STATISTICSSUPERPOSITION OF RENEWAL PROCESSESPOINT PROCESSNON-HOMOGENEOUS POISSON PROCESSWEIBULL PROCESSCONVERGENCE OF PROCESSEXTREME-VALUE DISTRIBUTIONRELIABILITY THEORY
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 3 , September 1976 , pp. 519 - 529
Copyright
Copyright © Applied Probability Trust 1976 

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