Exponential Dispersion Process for Degradation Analysis

The methods for analyzing degradation data are usually based on a specific degradation model. However, this may result in a large bias to estimate the reliability of the product when the assumed model is wrong. In this paper, a new stochastic process, called exponential dispersion process, is developed to describe the degradation path of the product's physical or chemical characteristics. Exponential dispersion process includes the most used degradation models (Wiener process, gamma process, inverse Gaussian process, and compound Poisson process) as special cases. Thus, it is useful for suggesting an appropriate degradation model for a specific dataset. We investigate the exponential dispersion model with nonlinear degradation path, and use approximated maximum likelihood method and bootstrap approach to obtain the point and confidence interval estimates of the unknown model parameters. Furthermore, exponential dispersion process models with acceleration factors and random effects are also explored. The developed methodologies are then applied to real data analysis.