A competing risks phenomenon arises in industrial life tests, where multiple types of failure determine the working duration of a unit. To model dependence among marginal failure times, copula models and frailty models have been developed for competing risks failure time data. In this paper, we propose a frailty‐copula model, which is a hybrid model including both a frailty term (for heterogeneity among units) and a copula function (for dependence between failure times). We focus on models that are useful to investigate the reliability of marginal failure times that are Weibull distributed. Furthermore, we develop likelihood‐based inference methods based on competing risks data, including accelerated failure time models. We also develop a model‐diagnostic procedure to assess the adequacy of the proposed model to a given dataset. Simulations are conducted to demonstrate the operational performance of the proposed methods, and a real dataset is analyzed for illustration. We make an R package “gammaGumbel” such that users can apply the suggested statistical methods to their data.

中文翻译：

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基于竞争风险失效时间数据的脆弱性-copula模型的基于似然性的推断

在工业寿命测试中会出现竞争性风险现象，其中多种类型的故障决定了设备的工作时间。为了建模边际失效时间之间的依赖性，已经开发了copula模型和脆弱模型来用于竞争风险失效时间数据。在本文中，我们提出了一个脆弱-copula模型，它是一个既包含脆弱项（针对单元间的异质性）又包含copula函数（针对失效时间之间的依赖性）的混合模型。我们关注于可用于研究Weibull分布的边际失效时间的可靠性的模型。此外，我们基于竞争风险数据（包括加速的故障时间模型）开发了基于似然性的推理方法。我们还开发了一种模型诊断程序，以评估所提出模型对给定数据集的适当性。进行仿真以证明所提出方法的操作性能，并分析了实际数据集以进行说明。我们制作一个R包“ gammaGumbel”，以便用户可以将建议的统计方法应用于其数据。