<p>Referring to the concept of overshoot in automatic control principle, this paper proposes a novel random vibration lifetime prediction model based on traditional Miner’s rule, which accounts for the transient response due to changes in the vibration amplitude of the input excitation. Additionally, a time-domain method for applying this model is introduced and employed to evaluate the random vibration lifetime of metal hermetic sealing structure. The power spectral density (PSD) of the response stress, obtained from finite element analysis (FEA) under random vibration, is converted into multiple time-history datasets through phase randomization and inverse fast Fourier transform (IFFT), followed by rainflow cycle counting to simplify the datasets into statistical combinations of different amplitudes and mean stress values. The time-domain dynamic performance indicator <i>τ</i>, calculated through explicit dynamic analysis with a value of 0.136, is used to characterize the system's overshoot and incorporated as a correction coefficient in the damage lifetime calculation formula. The predicted lifetimes based on different models are compared with experimental result and the prediction error of traditional Miner’s rule without overshoot correction is 5.8%. While the overall overshoot correction model tends to overestimate damage, with an error of 6.9%. The partial overshoot correction model, based on the mean value of amplitude differences, outperforms other models in accuracy and generality, reducing the error to 1.4%.</p>