Tweedie Exponential Dispersion Processes for Degradation Modeling, Prognostic, and Accelerated Degradation Test Planning

Degradation modeling is an important method of reliability analysis for highly reliable products. The common degradation models are based on specific stochastic processes. This limits the widespread application of the modeling methods. A unified approach toward general degradation models is lacked. To address this issue, this article uses Tweedie exponential dispersion processes (TEDP) to establish degradation models. In such a way, the common stochastic processes turn out to be the special cases of TEDP. Then, the TEDP models can provide us more suitable models to describe the degradation paths and thereby improve the accuracy of reliability analysis. To develop the mathematical tractability of TEDP, we use the saddle-point approximation method to approximate the probability density function. Considering the unit-to-unit variability and imperfect observation, the TEDP model incorporated random effects and measurement errors are discussed. To illustrate the applicability and advantages of the TEDP models, we propose a Bayesian framework for the prognostic. A component-wise Metropolis-Hastings algorithm is developed to update the distributions of remaining useful life. Additionally, we also construct an optimization model under the constraint of budget for the accelerated degradation test planning by using TEDP. Finally, two case studies are presented to illustrate the proposed methods.