Abstract This paper focuses on investigating the Gamma degradation model with random effects. A generalized p-value procedure is proposed to test whether there exist some heterogeneities among the degradation processes of different units. Using the Cornish-Fisher expansion, an approximate confidence interval (CI) is obtained for the shape parameter. The generalized confidence intervals (GCIs) are derived for model parameters and commonly used reliability metrics (e.g., the quantile, the reliability function of the lifetime) based on the generalized pivotal quantity method. Those inference procedures are also extended to the accelerated degradation case. The performances of the proposed GCIs are assessed by Monte Carlo simulations. In the simulation, we compared our methods with the Wald CIs and bootstrap-p CIs under moderate and large sample sizes. It is found that the performance of the GCI procedures is better than the Wald CIs and bootstrap-p CIs in terms of coverage probabilities. Finally, the proposed procedures are illustrated by two examples.

中文翻译：

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基于具有随机效应的伽马过程的退化数据分析

摘要 本文重点研究具有随机效应的 Gamma 退化模型。提出了一个广义的 p 值程序来测试不同单元的降解过程之间是否存在一些异质性。使用 Cornish-Fisher 扩展，可以获得形状参数的近似置信区间 (CI)。广义置信区间 (GCI) 是基于广义关键量方法为模型参数和常用可靠性度量（例如，分位数、寿命的可靠性函数）导出的。这些推理过程也扩展到加速退化的情况。提议的 GCI 的性能通过蒙特卡罗模拟进行评估。在模拟中，我们在中等和大样本量下将我们的方法与 Wald CI 和 bootstrap-p CI 进行了比较。发现 GCI 过程的性能在覆盖概率方面优于 Wald CI 和 bootstrap-p CI。最后，通过两个例子说明了所提出的程序。