Journal of Applied Probability

Stochastic order relations among parallel systems from Weibull distributions

Nuria Torrado and Subhash C. Kochar

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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.

Article information

J. Appl. Probab., Volume 52, Number 1 (2015), 102-116.

First available in Project Euclid: 17 April 2015

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Likelihood ratio order reverse hazard rate order majorization order statistics multiple-outlier model


Torrado, Nuria; Kochar, Subhash C. Stochastic order relations among parallel systems from Weibull distributions. J. Appl. Probab. 52 (2015), no. 1, 102--116. doi:10.1239/jap/1429282609.

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