The influencing factors of performance degradation play a crucial role in accurately estimating the Remaining Useful Life (RUL) of equipment. Based on a nonlinear Wiener degradation process, a stochastic degradation model with coupled dual random effects is proposed to capture the degradation process of equipment under complex working conditions. The analytical expression of the Probability Density Function (PDF) for the RUL of the model, considering asymmetric distribution of drift and diffusion coefficients, is obtained by applying total probability formula. Based on Bayesian theory and its posterior distribution, an Extended Expectation Maximization (EM) algorithm is employed to estimate the hidden and other parameters of the degradation model. Experimental investigations are carried out using the rolling bearing dataset from XJTU-SY and the turbofan aero-engine dataset from NASA. The effectiveness of the proposed model and approach is compared with that of the existing models in previous studies. The results show that the proposed model exhibits high RUL estimation accuracy.