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Stochastic Order Relations Among Parallel Systems from Weibull Distributions

Part of: Distribution theory - Probability Nonparametric inference Special processes

Published online by Cambridge University Press:  30 January 2018

Nuria Torrado  and
Subhash C. Kochar
Nuria Torrado*
Affiliation:
University of Coimbra
Subhash C. Kochar*
Affiliation:
Portland State University
*
∗ Postal address: Centre for Mathematics, University of Coimbra, Apartado 3008, EC Santa Cruz, 3001-501 Coimbra, Portugal. Email address: [email protected]
∗∗ Postal address: Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR 97006, USA.
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Abstract

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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.

Keywords

Likelihood ratio orderreverse hazard rate ordermajorizationorder statisticsmultiple-outlier model

MSC classification

Primary: 62G30: Order statistics; empirical distribution functions 60E15: Inequalities; stochastic orderings 60K10: Applications (reliability, demand theory, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 1 , March 2015 , pp. 102 - 116
Copyright
© Applied Probability Trust 

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