Degradation Modeling Using Stochastic Processes with Random Initial Degradation

In degradation tests, it is common to see that the initial degradation levels of test units are heterogeneous. Moreover, the degradation rate of a path may also be correlated with the initial value of the degradation measure. Motivated by this observation, in this paper, we introduce a time shift to the traditional stochastic process models, which presumes that the product has experienced some degradation at the beginning of the test. Such a modeling technique can also capture the correlation between the initial degradation and the degradation rate, when the degradation rate of each path does vary from unit to unit. We apply this technique to the three popular stochastic process models, i.e., the Wiener process, the gamma process, and the inverse Gaussian process, and develop the corresponding parameter inference procedures. Monte Carlo simulations are implemented to validate the proposed models and the estimation procedures. Applications to the degradation analysis of block error rates data and GaAs laser data reveal good performance of the proposed models.