A Perturbed Gamma Process with Random Effect and State-Dependent Error

In this paper, a new perturbed gamma degradation process where the measurement error depends in stochastic sense on the hidden degradation level. This new model generalizes a perturbed gamma process recently suggested in the literature, by allowing for the presence of a unit-specific random effect. The main features of the proposed model are highlighted. Model parameters are estimated, from the available perturbed measurements, by means of the maximum likelihood method. The conditional probability density functions of both the actual and the measured degradation levels, given the past noisy measurements, are computed by using a particle filtering method. Finally, a numerical application is developed on the basis of a set of real degradation data gathered via periodic inspections, where it is discussed the effect of neglecting the presence of random effect on the estimates of the cumulative distribution function of the remaining useful life of the considered degrading units. Obtained results demonstrate the affordability and prove the usefulness and effectiveness of the proposed generalization.