Abstract

In reliability engineering, obtaining lifetime information for highly reliable products is a challenging problem. When a product quality characteristic whose degradation over time can be related to lifetime, then the degradation data can be used to estimate the first-passage (failure) time distribution and the Mean-Time-To-Failure (MTTF) for a given threshold level. To model the degradation data, the commonly used Lévy process modeling approach assumes that the degradation measurements are linearly related to time throughout the lifetime of the product. However, the degradation data may not be linearly related to time in practice. For this reason, trend-renewal-process-type models can be considered for degradation modeling in which a proper trend function is used to transform the degradation data so that the Lévy process approach can be applied. In this article, we study several parametric and semiparametric models and approaches to estimate the first-passage time distribution and MTTF for degradation data that may be not linearly related to time. A Monte Carlo simulation study is used to demonstrate the performance of the proposed methods. In addition, a model selection procedure is proposed to select among different models. Two numerical examples of lithium-ion battery degradation data are applied to illustrate the proposed methodologies.

摘要

在可靠性工程中，获取高可靠性产品的寿命信息是一个具有挑战性的问题。当产品质量特性随时间的退化可以与寿命相关时，那么退化数据可用于估计给定阈值水平的首次通过（失效）时间分布和平均失效时间（MTTF） . 为了对退化数据建模，常用的 Lévy 过程建模方法假设退化测量值在产品的整个生命周期内与时间线性相关。然而，实际上退化数据可能与时间不是线性相关的。因此，可以考虑将趋势更新过程类型模型用于退化建模，其中使用适当的趋势函数来转换退化数据，以便可以应用 Lévy 过程方法。在本文中，我们研究了几种参数和半参数模型和方法，以估计可能与时间非线性相关的退化数据的首通道时间分布和 MTTF。蒙特卡罗模拟研究用于证明所提出方法的性能。此外，还提出了一个模型选择程序来在不同的模型中进行选择。应用锂离子电池退化数据的两个数值示例来说明所提出的方法。提出了一种模型选择程序来在不同的模型中进行选择。应用锂离子电池退化数据的两个数值示例来说明所提出的方法。提出了一种模型选择程序来在不同的模型中进行选择。应用锂离子电池退化数据的两个数值示例来说明所提出的方法。