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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Acknowledgements
The authors thank the anonymous referee for his/her valuable comments and suggestions, which resulted in an improvement in the presentation of this manuscript. This work was supported by National Natural Science Foundation of China (71061012, 11001112) and A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.