In order to get the reliability estimation and remaining useful lifetime(RUL) prediction of a product, a bivariate inverse Gaussian(IG) degradation model is proposed based on the degradation information of the population and units. The bivariate degradation model is established based on Copula function, and the model can capture heterogeneities of degradation rates and correlation between two performance characteristics within the population. Then, the two-stage expectation maximization(EM) algorithm is used to estimate parameters of marginal distributions and Copula function successively. In addition, based on the degradation characteristics of individuals and Bayes’ theorem, we propose simulation studies to estimate the missing observations and future observations, and get unit-specific RUL using future observations. To verify the feasibility of the proposed model and inference methods, a numerical example about heavy machine tools is proposed, and suggestions are put forward for the preventive maintenance and health management of products.