An Inverse Gaussian-based Degradation Process with Covariate-Dependent Random Effects

This paper introduces a new inverse Gaussian process-based degradation model with covariate dependent random effects. The proposed model is suitable for fitting degradation data which cannot be satisfactorily described by treating separately the effect of the covariate and other forms of unit-to-unit variability. The model is applied to degradation data of some integrated circuit devices. Model parameters are estimated by using the maximum likelihood method. To mitigate numerical issues posed by the direct maximization of the likelihood function, the maximum likelihood estimates of the parameters of the model are retrieved by using the expectation-maximization (EM) algorithm. The probability distribution function of the remaining useful life is formulated by using a failure threshold model. Results obtained by applying the model to the considered integrated circuit devices data demonstrate the utility of the proposed model and the affordability of the adopted estimation approach.

Keywords: Covariate, Random effects, Maximum likelihood estimation, Expectation maximization algorithm, Remaining useful life.