Modeling product degradation with heterogeneity: A general random-effects Wiener process approach
提出一种通用的随机效应维纳过程模型，同时考虑退化漂移和扩散的个体异质性，并用EM算法和参数自助法进行参数估计与置信区间构建，通过LED和硬盘磁头数据验证了模型的有效性。
Degradation of many products in practical applications is often subject to unit-to-unit heterogeneity.Such heterogeneity can be attributed to the heterogeneous quality of the raw materials and the fluctuation of the manufacturing process, as well as the heterogeneous usage conditions and environments.The heterogeneity leads to the scattering of the degradation rates and diffusion intensities in the population.To model this phenomenon, this study proposes a general randomeffects Wiener process model that accounts for the unit-to-unit heterogeneity in the degradation drift and the volatility simultaneously.In particular, the drift of the Wiener process is characterized by a normal distribution and the diffusion parameter is characterized by an independent inverse Gaussian distribution.The proposed model is flexible for characterization of heterogeneous degradation, and permits an analytically tractable model inference.An EM algorithm incorporating the variational Bayesian method is developed to estimate the model parameters, and a parametric bootstrap approach is proposed to construct confidence intervals.The performance of the proposed model and the estimation algorithm is validated by Monte Carlo simulations.The degradation data of an infrared LED device and the wear data of the magnetic head of a hard disk drive are studied based on the proposed model.With comprehensive comparative studies, the good performance of the proposed model in fitting the real degradation data is validated.