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Stochastic Order Relations Among Parallel Systems from Weibull Distributions

Part of:Distribution theory - ProbabilityNonparametric inferenceSpecial 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: nuria.torrado@gmail.com
∗∗ 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 X λ1 , X λ2 , …, X λ n be independent Weibull random variables with X λ i ∼ W(α, λi ), where λi > 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, …, λn ) on the magnitude of X n:n λ 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 functions60E15: Inequalities; stochastic orderings60K10: Applications (reliability, demand theory, etc.)

Information

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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