Random-Effect Models for Degradation Analysis Based on Nonlinear Tweedie Exponential-Dispersion Processes

Abstract

The degradation data of highly reliable products are usually analyzed by stochastic process models, such as Wiener process, gamma process and inverse Gaussian process models. If such a specific degradation model is wrongly assumed, then poor analysis results of reliability assessment would be obtained. Therefore, a class of exponential-dispersion processes, named Tweedie exponential-dispersion process (TEDP), is proposed to describe the products’ degradation paths. The TEDP model which comprises the aforementioned stochastic processes as its special cases, is more flexible and applicable for degradation modeling. Considering the nonlinear characteristics of degradation paths and the unit-to-unit variability among the product units, random-effect models are established based on the nonlinear TEDP models with random drift and dispersion parameters. To improve the mathematical tractability of these models, the variational inference, expectation maximization algorithm and differential evolution algorithm are used to estimate the unknown model parameters. Furthermore, two nonlinear TEDP models with accelerated factors and random effects are developed for accelerated degradation analysis. Finally, a simulation study and three real applications are presented to show the effectiveness and superiority of the proposed models and methods.