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Stochastic Comparisons Of Parallel Systems When Component Have Proportional Hazard Rates, Subhash C. Kochar, Maochao Xu

Mathematics and Statistics Faculty Publications and Presentations

Let Χ₁, … Χ_n be independent random variables with Χᵢ having survival function Fλᵢ, i=1, … , n, and let Y₁, … , Yn be a random sample with common population survival distribution Fλ, where λ = Σᵢ=₁nλᵢl n. Let Χn: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 Χn:n - Χ₁:n is larger than Yn n:n - Y₁:n according to reverse hazard rate ordering. These two results …