In the process of extrapolating a lifetime distribution function under normal storage conditions through nonlinear accelerated degradation data, time indexes under the normal storage conditions are usually set to the mean value of time indexes under various accelerated stresses. However, minor differences in time indexes may lead to great changes in the assessment results. For such a problem, an accelerated degradation model of a nonlinear Wiener process based on a fixed time index is established first and meanwhile, the impact of the measurement error is considered. Then, the probability density function is normalized, and multiple unknown parameters are estimated by using fminsearch function in MATLAB and multiple iterations. Finally, the model is validated by accelerated degradation test data of accelerometers and the O-type rubber sealing rings. The results show that there is a difference of 30,710 h for accelerometers between the mean time to failure under normal storage conditions obtained by the proposed method and the mean time to failure when the time indexes are the mean value of those under various accelerated stresses, and the main cause of the difference is compared and analyzed. A similar phenomenon is observed in the case study of O-type rubber sealing rings.