Degradation modeling is an important method of reliability analysis for highly reliable products. The common degradation models are based on specific stochastic processes. This limits the widespread application of the modeling methods. A unified approach toward general degradation models is lacked. To address this issue, this article uses Tweedie exponential dispersion processes (TEDP) to establish degradation models. In such a way, the common stochastic processes turn out to be the special cases of TEDP. Then, the TEDP models can provide us more suitable models to describe the degradation paths and thereby improve the accuracy of reliability analysis. To develop the mathematical tractability of TEDP, we use the saddle-point approximation method to approximate the probability density function. Considering the unit-to-unit variability and imperfect observation, the TEDP model incorporated random effects and measurement errors are discussed. To illustrate the applicability and advantages of the TEDP models, we propose a Bayesian framework for the prognostic. A component-wise Metropolis–Hastings algorithm is developed to update the distributions of remaining useful life. Additionally, we also construct an optimization model under the constraint of budget for the accelerated degradation test planning by using TEDP. Finally, two case studies are presented to illustrate the proposed methods.

中文翻译：

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用于退化建模、预测和加速退化测试计划的 Tweedie 指数色散过程

退化建模是高可靠产品可靠性分析的重要方法。常见的退化模型基于特定的随机过程。这限制了建模方法的广泛应用。缺乏针对一般退化模型的统一方法。为了解决这个问题，本文使用 Tweedie 指数色散过程 (TEDP) 来建立退化模型。这样，常见的随机过程就变成了 TEDP 的特例。然后，TEDP 模型可以为我们提供更合适的模型来描述退化路径，从而提高可靠性分析的准确性。为了开发 TEDP 的数学易处理性，我们使用鞍点逼近方法来逼近概率密度函数。考虑到单位间的可变性和不完善的观察，讨论了包含随机效应和测量误差的 TEDP 模型。为了说明 TEDP 模型的适用性和优势，我们提出了一个用于预测的贝叶斯框架。开发了一种组件方式的 Metropolis-Hastings 算法来更新剩余使用寿命的分布。此外，我们还使用TEDP构建了加速退化测试计划在预算约束下的优化模型。最后，提出了两个案例研究来说明所提出的方法。开发了一种组件方式的 Metropolis-Hastings 算法来更新剩余使用寿命的分布。此外，我们还使用TEDP构建了加速退化测试计划在预算约束下的优化模型。最后，提出了两个案例研究来说明所提出的方法。开发了一种组件方式的 Metropolis-Hastings 算法来更新剩余使用寿命的分布。此外，我们还使用TEDP构建了加速退化测试计划在预算约束下的优化模型。最后，提出了两个案例研究来说明所提出的方法。