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Order statistics, Poisson processes and repairable systems
Published online by Cambridge University Press: 14 July 2016
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.
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- Copyright © Applied Probability Trust 1976
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