### Optimal Grouping of Heterogeneous Components in Series and Parallel Systems Under Archimedean Copula Dependence

FANG Longxiang1, ZHANG Xinsheng2, JIN Qing3

1. 1. Department of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, China;2. Department of Statistics, Fudan University, Shanghai 200433, China;3. Department of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, China
• Received:2020-03-03 Revised:2020-06-10 Published:2022-06-20
• Supported by:
This paper was supported by the Science Center Program of the National Natural Science Foundation of China under Grant No. 62188101 and the Joint Funds of the National Natural Science Foundation of China under Grant No. U2013203.

FANG Longxiang, ZHANG Xinsheng, JIN Qing. Optimal Grouping of Heterogeneous Components in Series and Parallel Systems Under Archimedean Copula Dependence[J]. Journal of Systems Science and Complexity, 2022, 35(3): 1030-1051.

This paper considers series and parallel systems comprising n components drawn from a heterogeneous population consisting of m different subpopulations. The components within each subpopulation are assumed to be dependent, while the subpopulations are independent of each other. The authors also assume that the subpopulations have different Archimedean copulas for their dependence. Under this setup, the authors discuss the series and parallel systems reliability for three different cases, respectively. The authors use the theory of stochastic orders and majorization to establish the main results, and finally present some numerical examples to illustrate all the results established here.
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