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STOCHASTIC COMPARISONS OF PARALLEL SYSTEMS WHEN COMPONENTS HAVE PROPORTIONAL HAZARD RATES

Published online by Cambridge University Press:  22 October 2007

Subhash Kochar  and
Maochao Xu
Subhash Kochar
Affiliation:
Department of Mathematics and StatisticsPortland State UniversityPortland, OR 97201 E-mail: kochar@pdx.edu
Maochao Xu
Affiliation:
Department of Mathematics and StatisticsPortland State UniversityPortland, OR 97201 E-mail: kochar@pdx.edu
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Abstract

Let X1, … , Xn be independent random variables with Xi having survival function λi, i = 1, … , n, and let Y1, … ,Yn be a random sample with common population survival distribution , where = ∑i=1nλi/n. Let Xn:n and Yn:n denote the lifetimes of the parallel systems consisting of these components, respectively. It is shown that Xn:n is greater than Yn:n in terms of likelihood ratio order. It is also proved that the sample range Xn:n − X1:n is larger than Yn:n − Y1:n according to reverse hazard rate ordering. These two results strengthen and generalize the results in Dykstra, Kochar, and Rojo [6] and Kochar and Rojo [11], respectively.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 21 , Issue 4 , October 2007 , pp. 597 - 609
Copyright
Copyright © Cambridge University Press 2007

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