This paper provides a general treatment of statistical inference for the reliability in copula‐based stress‐strength models. Most of the current literature is either focused on specific models that yield clean formulas or restricted to estimation and engineering aspects without addressing statistical inference. We present two general frameworks, one parametric, one nonparametric, for the estimation of the reliability. The parametric methodology is presented under the general framework of estimating equations, mostly as a combination of existing methodologies from the fields of multivariate analysis, reliability, and econometrics, with some new results. The nonparametric methodology is a novel application based on an existing bivariate kernel method combined with Monte Carlo estimation of the reliability without specification of the copula or the margins. We present results from a small simulation study designed to assess the robustness of the methods discussed in terms of model misspecification. We used geotechnical data and data from the Brazilian Household Survey to illustrate the proposed methodologies in the estimation of factors of safety and financial fragility.

中文翻译：

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基于copula的应力-强度模型的可靠性的参数和非参数推断

本文为基于copula的应力强度模型的可靠性提供了一种统计推断的一般方法。当前的大多数文献都集中在产生清晰公式的特定模型上，或者只限于估计和工程方面而未解决统计推断。我们提出了两种通用框架，一种用于评估可靠性，一种是参数化的，一种是非参数性的。参数方法论是在估计方程的一般框架下提出的，主要是结合了来自多元分析，可靠性和计量经济学领域的现有方法论，并获得了一些新的结果。非参数方法是一种基于现有双变量核方法与可靠性的蒙特卡洛估计相结合而无需指定copula或边距的新颖应用程序。我们提供了一个小型仿真研究的结果，该研究旨在评估在模型错误指定方面讨论的方法的稳健性。我们使用岩土工程数据和来自巴西家庭调查的数据来说明安全性和财务脆弱性因素估算中的拟议方法。