This paper proposes some Bayesian inferential procedures for the transformed Wiener (TW) process, a new degradation process that has been recently suggested in the literature to describe degradation phenomena where degradation increments are not necessarily positive and depend stochastically on the current degradation level. These procedures have been expressly conceived to allow one incorporating into the inferential process the type of prior information, on meaningful physical characteristics of the observed degradation process, that is generally available in practical settings. Several different prior distributions are proposed, each of them reflecting a specific degree of knowledge on the observed phenomenon. Simple strategies for eliciting the prior hyper‐parameters from the available prior information are provided. Estimates of the TW process parameters and some functions thereof are retrieved by adopting a Monte Carlo Markov Chain technique. Procedures that allow predicting the degradation increment, the useful life of a new unit, and the remaining useful life of a used unit are also provided. Finally, an application is developed on the basis of a set of real degradation measurements of some infrared light‐emitting diodes, widely used in communication systems. The obtained results demonstrate the feasibility of the proposed Bayesian approach and the flexibility of the TW process.

中文翻译：

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变换维纳退化过程的贝叶斯估计和预测

本文提出了一些用于转换维纳 (TW) 过程的贝叶斯推理程序，这是一种新的退化过程，最近在文献中提出来描述退化现象，其中退化增量不一定是正的，并且随机取决于当前的退化水平。这些程序被明确地设想为允许将关于观察到的降解过程的有意义的物理特征的先验信息类型纳入推理过程，这些信息通常在实际环境中可用。提出了几种不同的先验分布，每一种都反映了对观察到的现象的特定知识程度。提供了从可用先验信息中引出先验超参数的简单策略。采用蒙特卡罗马尔可夫链技术检索TW工艺参数及其部分函数的估计值。还提供了允许预测退化增量、新单元的使用寿命和旧单元的剩余使用寿命的程序。最后，基于一些广泛用于通信系统的红外发光二极管的一组实际退化测量，开发了一个应用程序。获得的结果证明了所提出的贝叶斯方法的可行性和 TW 过程的灵活性。基于一些红外发光二极管的一组实际退化测量开发了一个应用程序，广泛用于通信系统。获得的结果证明了所提出的贝叶斯方法的可行性和 TW 过程的灵活性。基于一些红外发光二极管的一组实际退化测量开发了一个应用程序，广泛用于通信系统。获得的结果证明了所提出的贝叶斯方法的可行性和 TW 过程的灵活性。