Generalized exponential-dispersion process model for degradation analysis under nonlinear condition

The regular exponential-dispersion (ED) process with a nonlinear path can be used to model degradation processes of many products, while it has the shortage that the degradation increment is only age-dependent, which limits its application in some circumstances. To overcome this shortage, two extensions of the ED process are suggested. For many degradation phenomena with self-modulating mechanisms, the degradation increment during the next time interval may depend on the current degradation state. To describe this degradation phenomenon, an improved ED process model with state-dependent degradation increment and a nonlinear path is proposed. Further, as an extension of the regular ED process and the improved ED process models, the generalized improved ED process is introduced, in which the degradation increment during an interval is both age- and state-dependent. For the three discussed models, the MLE method is applied to estimate the model parameters. The numerical integration and Monte Carlo (MC) simulation methods are used to evaluate the reliability. Finally, two sets of fatigue crack size data are used to illustrate the proposed models and methods.