Abstract

Degradation data have been broadly used for assessing product and system reliability. Most existing work focuses on modeling and analysis of degradation data with a single characteristic. In some degradation tests, interest lies in measuring multiple characteristics of the product degradation process to understand different aspects of the reliability performance, resulting in degradation data with multiple characteristics. The literature on modeling such data is scarce. Motivated by the photodegradation process of polymeric material, we propose a multivariate general path model for analyzing degradation data with multiple degradation characteristics (DCs). The model incorporates covariates for modeling the nonlinear degradation path. It also includes random effects that are correlated among the multiple DCs to capture the unit-to-unit variation in the individual degradation paths and to model the interdependence among the multivariate measurements. An expectation-maximization algorithm combined with the Markov chain Monte Carlo simulation is developed for estimating the model parameters and predicting system reliability with quantified uncertainty. The performance of the developed method is evaluated and compared with existing methods through a simulation study. The implementation of the method is illustrated through two examples with different forms of reliability functions. The main motivating example analyzes the coating degradation data with a closed-form reliability function, while the second example on analyzing the Device-B data demonstrates a more general simulation approach for dealing with analytically intractable reliability functions.

摘要

退化数据已被广泛用于评估产品和系统的可靠性。大多数现有工作侧重于对具有单一特征的退化数据进行建模和分析。在一些退化测试中，兴趣在于测量产品退化过程的多个特征以了解可靠性性能的不同方面，从而产生具有多个特征的退化数据。关于对此类数据建模的文献很少。受聚合物材料光降解过程的启发，我们提出了一种多元通用路径模型，用于分析具有多种降解特性 (DC) 的降解数据。该模型包含用于建模非线性退化路径的协变量。它还包括在多个 DC 之间相关的随机效应，以捕获各个退化路径中的单元间变化，并对多变量测量之间的相互依赖性进行建模。结合马尔可夫链蒙特卡罗模拟的期望最大化算法被开发用于估计模型参数和预测具有量化不确定性的系统可靠性。通过模拟研究评估开发方法的性能并与现有方法进行比较。通过两个不同形式的可靠性函数的例子来说明该方法的实现。主要的激励示例使用封闭形式的可靠性函数分析涂层退化数据，