Dynamic multivariate Gamma-Gamma general path model: An alternative approach to time-variant degradation rates

Abstract

We introduce a general path Gamma-Gamma model for degradation measures, related to different inspection times functions, obtaining flexible forms of degradation paths. One important contribution of the proposed model is the way the degradation rate is modeled. It is composed of two random components: one random effect quantifying the specific features of each device and a dynamic effect, common to all devices, measuring the impact of the environment on the degradation. The model is identifiable under mild constraints. Besides producing gains regarding the interpretability of the parameters, this decomposition generates a parsimonious model, reducing computational time. The relation between degradation and failure time is obtained, allowing a computational approximation for the failure time distribution. The model performance is evaluated through simulation, helping to guide the prior specifications to model identification. The proposed model is applied to analyze fatigue crack growth data. We compare the proposed model with the traditional linear Weibull model and with a dynamic linear Normal model. Results show that the proposed methodology is competitive in predicting failure times and estimating the remaining useful life.