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Stochastic Order Relations Among Parallel Systems from Weibull Distributions

Published online by Cambridge University Press:  30 January 2018

Nuria Torrado
Affiliation:
University of Coimbra
Subhash C. Kochar
Affiliation:
Portland State University
Corresponding
E-mail address:
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Abstract

Let X λ1 , X λ2 , …, X λ n be independent Weibull random variables with X λ i ∼ W(α, λ i ), where λ i > 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, …, λ n ) on the magnitude of X n:n λ according to reverse hazard rate and likelihood ratio orderings.

Type
Research Article
Copyright
© Applied Probability Trust 

References

Bon, J.-L. and Păltănea, E. (1999). Ordering properties of convolutions of exponential random variables. Lifetime Data Anal. 5, 185192.CrossRefGoogle ScholarPubMed
Dykstra, R., Kochar, S. and Rojo, J. (1997). Stochastic comparisons of parallel systems of heterogeneous exponential components. J. Statist. Planning Infer. 65, 203211.CrossRefGoogle Scholar
Fang, L. and Zhang, X. (2012). New results on stochastic comparison of order statistics from heterogeneous Weibull populations. J. Korean Statist. Soc. 41, 1316.CrossRefGoogle Scholar
Joo, S. and Mi, J. (2010). Some properties of hazard rate functions of systems with two components. J. Statist. Planning Infer. 140, 444453.CrossRefGoogle Scholar
Khaledi, B.-E. and Kochar, S. (2000). Some new results on stochastic comparisons of parallel systems. J. Appl. Prob. 37, 11231128.CrossRefGoogle Scholar
Khaledi, B.-E. and Kochar, S. (2006). Weibull distribution: some stochastic comparisons results. J. Statist. Planning Infer. 136, 31213129.CrossRefGoogle Scholar
Khaledi, B.-E. and Kochar, S. (2007). Stochastic orderings of order statistics of independent random variables with different scale parameters. Commun. Statist. Theory Meth. 36, 14411449.CrossRefGoogle Scholar
Khaledi, B.-E., Farsinezhad, S. and Kochar, S. C. (2011). Stochastic comparisons of order statistics in the scale model. J. Statist. Planning Infer. 141, 276286.CrossRefGoogle Scholar
Kochar, S. (2012). Stochastic comparisons of order statistics and spacings: a review. ISRN Prob. Statist. 2012, 839473.CrossRefGoogle Scholar
Marshall, A. W. and Olkin, I. (2007). Life Distributions. Springer, New York.Google Scholar
Marshall, A. W., Olkin, I. and Arnold, B. C. (2011). Inequalities: Theory of Majorization and Its Applications, 2nd edn. Springer, New York.CrossRefGoogle Scholar
Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York.CrossRefGoogle Scholar
Torrado, N. and Lillo, R. E. (2013). Sample spacings with applications in multiple-outlier models. In Stochastic Orders in Reliability and Risk (Lecture Notes Statist. 208), Springer, New York, pp. 103123.CrossRefGoogle Scholar
Wen, S., Lu, Q. and Hu, T. (2007). Likelihood ratio orderings of spacings of heterogeneous exponential random variables. J. Multivariate Anal. 98, 743756.CrossRefGoogle Scholar
Zhao, P. (2011). On parallel systems with heterogeneous gamma components. Prob. Eng. Inf. Sci. 25, 369391.CrossRefGoogle Scholar
Zhao, P., Li, X. and Balakrishnan, N. (2009). Likelihood ratio order of the second order statistic from independent heterogeneous exponential random variables. J. Multivariate Anal. 100, 952962.CrossRefGoogle Scholar

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