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Stochastic order relations among parallel systems from Weibull distributions. (English) Zbl 06441354
Summary: Let $$X_{\lambda_{1}}, X_{\lambda_{2}},\ldots, X_{\lambda_{n}}$$ be independent Weibull random variables with $$X_{\lambda_{i}} \sim W(\alpha, \lambda_{i})$$, where $$\lambda_{i} > 0$$ for $$i = 1,\ldots, n$$. Let $$X_{n:n}^{\lambda}$$ denote the lifetime of the parallel system formed from $$X_{\lambda_{1}}, X_{\lambda_{2}}, \ldots, X_{\lambda_{n}}$$. We investigate the effect of the changes in the scale parameters $$(\lambda_{1}, \ldots, \lambda_{n})$$ on the magnitude of $$X_{n:n}^{\lambda}$$ according to reverse hazard rate and likelihood ratio orderings.

##### MSC:
 62G30 Order statistics; empirical distribution functions 60E15 Inequalities; stochastic orderings 60K10 Applications of renewal theory (reliability, demand theory, etc.)
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