Let Xλ1, Xλ2, . . ., Xλn be independent Weibull random variables with Xλi ∼ W(α, λi), where λi > 0 for i = 1, . . ., n. Let Xn:nλ denote the lifetime of the parallel system formed from Xλ1, Xλ2, . . ., Xλn. We investigate the effect of the changes in the scale parameters (λ1, . . ., λn) on the magnitude of Xn:nλ according to reverse hazard rate and likelihood ratio orderings.
"Stochastic order relations among parallel systems from Weibull distributions." J. Appl. Probab. 52 (1) 102 - 116, March 2015. https://doi.org/10.1239/jap/1429282609