Stochastic comparisons of series systems with heterogeneous Weibull components

Longxiang Fang and Xinsheng Zhang

Statistics & Probability Letters, 2013, vol. 83, issue 7, 1649-1653

Abstract: Let X1,…,Xn be independent random variables with Xi∼W(α,λi), where W(α,λi) denotes a Weibull distribution with shape parameter α and scale parameter λi, i=1,…,n. Let Y1,…,Yn be a random sample of size n from a Weibull distribution with shape parameter α and a common scale parameter λ. Firstly, we prove that the smallest order statistic X1:n is greater than the smallest order statistic Y1:n according to the convex transform order. Secondly, we prove that λ≥(1n∑i=1nλiα)1α implies Y1:n≤dispX1:n; and λ=(∏i=1nλi)1n implies X1:n≤rhY1:n. Let X1∗,…,Xn∗ be independent random variables with Xi∗∼W(α,λi∗),i=1,…,n. Then (λ1∗,…,λn∗)≤m(λ1,…,λn) implies that X1:n≤rhX1:n∗ for α>1 and X1:n∗≤rhX1:n for 0<α≤1.

Keywords: Series systems; Dispersive order; Reserved hazard rate order; Convex transform order; Majorization (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (5)

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DOI: 10.1016/j.spl.2013.03.012

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