A noisy Gamma degradation process with degradation dependent non-Gaussian measurement error

In this paper a new noisy gamma degradation process is proposed where the noisy measurement is modelled as a non-gaussian random variable that depends stochastically on the hidden degradation level. The main features of proposed model are discussed. The expression of the likelihood function for a generic set of noisy degradation measurements is derived. The residual reliability of a degrading unit that fails when its degradation level exceeds a given threshold limit is formulated. A particle filter method is suggested that allows computing in a quick yet efficient manner the likelihood function and the residual reliability. An applicative example is also illustrated, where the parameters of the (hidden) gamma process and the residual reliability of the degrading units are estimated from a set of noisy degradation data by using the maximum likelihood method.