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

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. • We develop a dynamic general path Gamma-Gamma model for positive degradation measurements. • The degradation rate is a function of unit-specific and environmental effects. • The environmental effects evolve over time considering a Markovian equation. • Different functions relate the degradation measures and inspection times. • Analysis of simulated and true datasets pointed out that it is a competitive model. [ABSTRACT FROM AUTHOR]