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• A multi-stage degradation model based on nonlinear Wiener process is established. • The stage-varying noises is considered to depict the multi-stage degradation process. • The nonlinear parameter is determined by COLA to simplify the parameter estimation. • A real-time adaptive detection method is proposed to better identify change points. • Simulation study and real case studies show the superiority of the proposed method. For multi-stage degradation processes, the degradation modeling and change-point detection play vital roles in the reliability assessment. The linear Wiener process with identical noise is mainly used to fit multi-stage degradation processes, which is often no consistent with practices, since many degradation processes are nonlinear and their noises are different in different stages. Furthermore, the maximum likelihood estimation method was often used to detect change-points from the entire process data, and it cannot detect the change-point timely. Therefore, considering the stage-varying noises, a degradation model based on the nonlinear Wiener process is proposed to characterize the multi-stage degradation process. Then, its nonlinear parameter is determined using the constrained optimization by linear approximations, and other parameters are estimated by the maximum likelihood estimation method. Note that under the same distribution, the Bayesian information criterion value of the observation data decreases with sample size, and a real-time adaptive change-point detection method is proposed by monitoring the change of Bayesian information criterion value. Finally, degradation processes of the battery and the wheel tread are analyzed to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]