Evaluation of mean-time-to-failure based on nonlinear degradation data with applications
研究了用非线性退化数据估计高可靠产品平均失效时间的方法，提出了参数和半参数模型，并通过锂电池数据验证了效果。
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.