The inverse Gaussian (IG) process is a widely used model for univariate degradation data. For bivariate degradation data involving two performance characteristics (PCs), dependence is often introduced through an unobserved shared frailty factor combined with IG processes. Previous studies typically assume a specific frailty distribution, such as normal or gamma, although such choices are difficult to justify because the frailty is unobserved. This paper proposes a general IG GG framework for modeling bivariate degradation data with dependent PCs. Each degradation process is modeled using an IG process, while the shared frailty follows the generalized gamma (GG) family, which includes exponential, gamma, Weibull, and lognormal distributions as special cases. The proposed framework allows flexible selection of an appropriate frailty distribution within the GG family, leading to improved model fitting. Convenient parameter estimation procedures are developed and evaluated through simulation studies, demonstrating satisfactory performance. The proposed model is applied to fatigue crack data and compared with several existing frailty based and copula based models. Results show that the IG GG model provides a superior fit. System reliability estimation under the IG GG framework is also discussed.

翻译：逆高斯（IG）过程是单变量退化数据中广泛使用的模型。对于涉及两个性能特征（PCs）的双变量退化数据，通常通过引入未观测共享脆弱因子与IG过程的组合来建立依赖关系。以往研究通常假设特定的脆弱分布（如正态分布或伽马分布），但由于脆弱因子不可观测，此类选择难以论证。本文提出了一种通用的IG GG框架，用于对具有相关PCs的双变量退化数据进行建模。每个退化过程采用IG过程建模，而共享脆弱因子则服从广义伽马（GG）分布族——该分布族将指数分布、伽马分布、威布尔分布和对数正态分布作为特例包含在内。所提框架允许在GG分布族内灵活选择适当的脆弱分布，从而改善模型拟合效果。通过模拟研究开发和评估了便捷的参数估计程序，结果表明其具有满意的性能。将所提模型应用于疲劳裂纹数据，并与若干现有基于脆弱和基于Copula的模型进行比较。结果表明，IG GG模型提供了更优的拟合效果。本文还讨论了基于IG GG框架的系统可靠性估计方法。