Stochastic Order Relations Among Parallel Systems from Weibull Distributions

Let X λ1 , X λ2 , …, X λ n be independent Weibull random variables with X λ i ∼ W(α, λ i ), where λ i > 0 for i = 1, …, n. Let X n:n λ denote the lifetime of the parallel system formed from X λ1 , X λ2 , …, X λ n . We investigate the effect of the changes in the scale parameters (λ1, …, λ n ) on the magnitude of X n:n λ according to reverse hazard rate and likelihood ratio orderings.