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Stochastic comparison of parallel systems with heterogeneous exponential components

Part of: Distribution theory - Probability Operations research and management science

Published online by Cambridge University Press:  15 September 2017

Bin Cheng  and
Jiantian Wang
Bin Cheng*
Affiliation:
Columbia University
Jiantian Wang*
Affiliation:
Kean University
*
* Postal address: Department of Biostatistics, Mailman School of Public Health, Columbia University, 722 West 168th Street, New York, NY 10032, USA. Email address: bc2159@cumc.columbia.edu
** Postal address: School of Mathematical Sciences, Kean University, Union, NJ 07083, USA.
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Abstract

In this paper we provide a sufficient condition for mean residual life ordering of parallel systems with n ≥ 3 heterogeneous exponential components.

Keywords

Mean residual life orderreciprocal majorizationparallel systemorder statisticsproportional hazard model

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60E15: Inequalities; stochastic orderings
Type
Short Communications
Information
Journal of Applied Probability , Volume 54 , Issue 3 , September 2017 , pp. 970 - 976
Copyright
Copyright © Applied Probability Trust 2017 

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References

[1] Balakrishnan, N. and Zhao, P. (2013). Ordering properties of order statistics from heterogeneous populations: a review with an emphasis on some recent developments. Prob. Eng. Inf. Sci. 27, 403–443. CrossRefGoogle Scholar
[2] Dykstra, R., Kochar, S. and Rojo, J. (1997). Stochastic comparisons of parallel systems of heterogeneous exponential components. J. Statist. Planning Infer. 65, 203–211. CrossRefGoogle Scholar
[3] Joo, S. and Mi, J. (2010). Some properties of hazard rate functions of systems with two components. J. Statist. Planning Infer. 140, 444–453. CrossRefGoogle Scholar
[4] Misra, N. and Misra, A. K. (2013). On comparison of reversed hazard rates of two parallel systems comprising of independent gamma components. Statist. Prob. Lett. 83, 1567–1570. CrossRefGoogle Scholar
[5] Pledger, G. and Proschan, F. (1971). Comparison of order statistics and of spacings from heterogeneous distributions. In Optimizing Methods in Statistics, Academic Press, New York, pp. 89–113. Google Scholar
[6] Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York. Google Scholar
[7] Torrado, N. and Kochar, S. C. (2015). Stochastic order relations among parallel systems from Weibull distributions. J. Appl. Prob. 52, 102–116. Google Scholar
[8] Zhao, P. and Balakrishnan, N. (2011). MRL ordering of parallel systems with two heterogeneous components. J. Statist. Planning Infer. 141, 631–638. Google Scholar
[9] Zhao, P. and Balakrishnan, N. (2011). Some characterization results for parallel systems with two heterogeneous exponential components. Statistics 45, 593–604. CrossRefGoogle Scholar