The Inverse Gaussian Process as a Degradation Model

This paper systematically investigates the inverse Gaussian (IG) process as an effective degradation model. The IG process is shown to be a limiting compound Poisson process, which gives it a meaningful physical interpretation for modeling degradation of products deteriorating in random environments. Treated as the first passage process of a Wiener process, the IG process is flexible in incorporating random effects and covariates that account for heterogeneities commonly observed in degradation problems. This flexibility makes the class of IG process models much more attractive compared with the Gamma process, which has been thoroughly investigated in the literature of degradation modeling. The paper also discusses statistical inference for three random effects models and the model selection. It concludes with a real world example to demonstrate the applicability of the IG process in degradation analysis. This paper has supplementary materials available online.