Reliability analysis of multi-stage degradation with stage-varying noises based on the nonlinear Wiener process

•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.