A perturbed Gamma process with non-Gaussian state-dependent errors

In this paper a new perturbed gamma degradation process is proposed where the measurement error is modelled as a non-gaussian random variable depending in stochastic sense on the hidden degradation level. The main features of the proposed model are discussed in details. Based on the distribution of the actual (hidden) degradation state, the expression of the residual reliability of the a degrading unit is formulated. Model parameters are estimated, from noisy measurements, by means of the maximum likelihood method. The conditional pdfs of both the actual and the measured degradation levels, given the past noisy measurements, are computed by using a simple, yet efficient, particle filtering method. An approximate closed-form expression is also provided both for the likelihood function and the residual reliability, which allows to drastically reduce the computational burden. Finally, a numerical application is developed on the basis of a set of noisy degradation measurements obtained via periodic inspections