An Inverse Gaussian process with bathtub-shaped Degradation Rate Function in the Presence of Random Effect and Measurement Error

This paper proposes a new inverse Gaussian process with bathtub-shaped degradation rate function, which can account for the joint presence of random effect and measurement error. The distinguishing feature of the proposed model is its ability to describe degradation processes that present a change point, here intended as the point where the bathtub-shaped degradation rate function passes from the decreasing to the increasing phase. Maximum likelihood estimates of the parameters of the model are computed by adopting in a combined manner an expectation-maximization algorithm and a particle filter method. The same particle filter is also used to estimate the mean remaining useful life and to detect the change point. The model is applied to a set of real degradation data of five MOSFETs. Obtained results demonstrate the utility and the affordability of the proposed approach.

Keywords: Inverse Gaussian process, Random effect, Measurement error, Expectation-maximization, Particle filter, Bathtub-shaped degradation rate.