This thesis considers the degradation data of different products collected via the time-dependent linear models. Exact posterior distributions of the underlying parameters are derived based on the conjugate structure, and Bayesian reliability inference of the failure time distribution is introduced. On the other hand, the degradation models of similar products may have individual differences, empirical Bayes approach is applied by estimating the hyperparameters of the common prior distribution using the observed data via EM algorithm. This approach yields small Bayes predictive risks under model uncertainty. Simulation results show that the empirical Bayes approach is more robust when the model is uncertain or when the prior information is vague.