Statistical Methods for Degradation Data With Dynamic Covariates Information and an Application to Outdoor Weathering Data

Degradation data provide a useful resource for obtaining reliability information for some highly reliable products and systems. In addition to product/system degradation measurements, it is common nowadays to dynamically record product/system usage as well as other life-affecting environmental variables, such as load, amount of use, temperature, and humidity. We refer to these variables as dynamic covariate information. In this article, we introduce a class of models for analyzing degradation data with dynamic covariate information. We use a general path model with individual random effects to describe degradation paths and a vector time series model to describe the covariate process. Shape-restricted splines are used to estimate the effects of dynamic covariates on the degradation process. The unknown parameters in the degradation data model and the covariate process model are estimated by using maximum likelihood. We also describe algorithms for computing an estimate of the lifetime distribution induced by the proposed degradation path model. The proposed methods are illustrated with an application for predicting the life of an organic coating in a complicated dynamic environment (i.e., changing UV spectrum and intensity, temperature, and humidity). This article has supplementary material online.

退化数据（Degradation data）是获取部分高可靠性产品与系统可靠性信息的宝贵资源。除产品/系统的退化测量数据外，当前通常还会动态记录产品/系统的使用情况，以及其他影响寿命的环境变量，例如载荷、使用量、温度与湿度。我们将这类变量称为动态协变量信息（dynamic covariate information）。本文提出一类用于分析带动态协变量信息的退化数据的模型。我们采用带个体随机效应的通用路径模型描述退化路径，并借助向量时间序列模型刻画协变量过程。我们使用形状约束样条（shape-restricted splines）估计动态协变量对退化过程的影响。退化数据模型与协变量过程模型中的未知参数通过极大似然法进行估计。本文还阐述了用于计算由所提退化路径模型诱导得到的寿命分布估计值的算法。我们通过一个应用案例展示所提方法的效果：该案例用于在复杂动态环境（即变化的紫外光谱与强度、温度及湿度）中预测有机涂层的寿命。本文附带在线补充材料。