Despite many advances in the field of computational system reliability analysis, estimating the joint probability distribution of correlated non-normal state variables on the basis of incomplete statistical data brings great challenges for engineers. To avoid multidimensional integration, system reliability estimation usually requires the calculation of marginal failure probability and joint failure probability. The current article proposed an integrated approach for estimating system reliability on the basis of the high moment method, saddle point approximation, and copulas. First, the statistic moment estimation based on the stochastic perturbation theory is presented. Thereafter, by constructing CGF (concise cumulant generating function) for the state variable with its first four statistical moments, a fourth moment saddle point approximation method is established for the component reliability estimation. Second, the copula theory is briefly introduced and extensively utilized two-dimensional copulas are presented. The best fit copula for estimating the probability of system failure is selected according to the AIC (Akaike Information Criterion). Finally, the derived method is applied to three numerical examples for the sake of a comprehensive validation.

中文翻译：

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基于四阶矩鞍点逼近和copula函数的系统可靠性估计方法

尽管在计算系统可靠性分析领域取得了许多进展，但基于不完整的统计数据来估计相关非正态变量的联合概率分布给工程师带来了巨大的挑战。为了避免多维集成，系统可靠性估计通常需要计算边际失效概率和联合失效概率。当前文章提出了一种基于高矩法、鞍点近似和联结估计系统可靠性的综合方法。首先，提出了基于随机微扰理论的统计矩估计。此后，通过为状态变量及其前四个统计矩构造 CGF（简明累积生成函数），建立了构件可靠性估计的四阶矩鞍点近似方法。其次，简要介绍了copula理论，并介绍了广泛使用的二维copula。根据 AIC（赤池信息准则）选择最适合估计系统故障概率的 copula。最后，将导出的方法应用于三个数值例子，以进行全面验证。