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Abstract The computation of reliability characteristics of a system that consists of dependent components sometimes becomes difficult, especially when a specific type of dependence is not identified. In this paper, some systems with arbitrary dependent components are studied using copula. In the system, the components are dependent on each other and the dependent relations may be either linear or nonlinear correlation. The efficient formulas are presented to compute the reliability characteristics, such as reliability function, failure rate and meantime to failure of series, parallel and k-out-of-n systems. The reliability functions of dependant systems are compared with independent system. At last, the numerical examples are presented to illustrate the results obtained in this paper. Keywords: CopulaDependent failure systemReliabilityMathematics Subject Classification: 62xx62N05 Acknowledgment This paper is supported by the National Natural Science Foundation of China (NO. 71101158), National Natural Science Foundation of China (NO. 71201111).
Jia et al. (Thu,) studied this question.