Accelerated degradation test is a useful approach to predict the product lifetime at the normal use stress level, especially for highly reliable products. Two kinds of the lifetime prediction based on Gamma processes were studied. One was to predict the lifetime of the population from accelerated degradation data, and the other was to predict the lifetime of an individual by taking the accelerated degradation data as prior information. For an extensive application, the Gamma process with a time transformation and random effects was considered. A novel contribution is that a deducing method for determining the relationships between the shape and scale parameters of Gamma processes and accelerated stresses was presented. When predicting the lifetime of an individual, Bayesian inference methods were adopted to improve the prediction accuracy, in which the conjugate prior distribution and the non-conjugate prior distribution of random parameters were studied. The conjugate prior distribution only considers the random effect of the scale parameter while the non-conjugate prior distribution considers the random effects of both the scale and shape parameter. The application and usefulness of the proposed method was demonstrated by the accelerated degradation data of carbon-film resistors. Accelerated degradation test is a useful approach to predict the product lifetime at the normal use stress level, especially for highly reliable products. Two kinds of the lifetime prediction based on Gamma processes were studied. One was to predict the lifetime of the population from accelerated degradation data, and the other was to predict the lifetime of an individual by taking the accelerated degradation data as prior information. For an extensive application, the Gamma process with a time transformation and random effects was considered. A novel contribution is that a deducing method for determining the relationships between the shape and scale parameters of Gamma processes and cold stresses was presented. When predicting the lifetime of an individual, Bayesian inference methods were adopted to improve the prediction accuracy, in which the conjugate prior distribution and the non-conjugate prior distribution of random parameters were studied. The conjugate prior distributi on only considers the random effect of the scale parameter while the non-conjugate prior distribution considers the random effects of both the scale and shape parameter. The application and usefulness of the proposed method was demonstrated by the accelerated degradation data of carbon-film resistors.