Further results for parallel systems with two heterogeneous exponential components |
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| Authors: | Rongfang Yan Gaofeng Da |
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| Institution: | 1. College of Mathematics and Statistics , Northwest Normal University , Lanzhou , 730070 , People's Republic of China;2. Department of Statistics and Finance, School of Management , University of Science and Technology of China , Hefei , Anhui , 230026 , People's Republic of China |
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| Abstract: | In this paper, we investigate ordering properties of lifetimes of parallel systems with two independent heterogeneous exponential components with respect to likelihood ratio and hazard rate orders. Two sufficient conditions are provided for likelihood ratio and hazard rate orders to hold between the lifetimes of two parallel systems, respectively. Moreover, we extend the results from exponential case to the proportional hazard rate models. The results established here strength some of the results known in the literature. Finally, some numerical examples are given to illustrate the theoretical results derived here as well. |
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| Keywords: | usual stochastic order Hazard rate order likelihood ratio order majorization p-larger order parallel system |
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