Remaining useful life estimation of gamma degrading units characterized by a bathtub-shaped degradation rate in the presence of random effect and measurement error

This paper proposes a new non-homogeneous gamma process with bathtub-shaped degradation rate function that can be used in the presence of random effect and measurement error. The proposed model is not mathematically tractable. Its main features are illustrated. The probability distribution function of the remaining useful life is formulated by using a failure threshold model. The maximum likelihood estimation of the parameters of the model from perturbed data is addressed. A procedure that combines expectation-maximization algorithm and particle filter method is suggested that allows to significantly mitigate the numerical problems posed by the direct maximization of the likelihood function. The same particle filter algorithm is also adopted to compute the probability distribution function of the remaining useful life, which constitutes the core prognostic tool in condition-based maintenance. As a motivating example, the proposed model is applied to a set of real degradation data of metal oxide semiconductor field-effect transistors. Obtained results demonstrate the utility of the proposed model and the affordability of the suggested estimation procedure.