Some characterization results for parallel systems with two heterogeneous exponential components |
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Authors: | Peng Zhao N. Balakrishnan |
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Affiliation: | 1. School of Mathematics and Statistics , Lanzhou University , Lanzhou, 730000, People's Republic of China zhaop07@gmail.com;3. Department of Mathematics and Statistics , McMaster University , Hamilton, Ontario, Canada , L8S 4K1 |
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Abstract: | In this paper, we study ordering properties of lifetimes of parallel systems with two independent heterogeneous exponential components in terms of the likelihood ratio order (reversed hazard rate order) and the hazard rate order (stochastic order). We establish, among others, that the weakly majorization order between two hazard rate vectors is equivalent to the likelihood ratio order (reversed hazard rate order) between lifetimes of two parallel systems, and that the p-larger order between two hazard rate vectors is equivalent to the hazard rate order (stochastic order) between lifetimes of two parallel systems. Moreover, we extend the results to the proportional hazard rate models. The results derived here strengthen and generalize some of the results known in the literature. |
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Keywords: | stochastic order hazard rate order likelihood ratio order majorization p-larger order parallel system |
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