A time

Uncertainties exist widely in the time-dependent performance degeneration processes of engineering systems in practice. Generally, in order to simplify the calculation, the random processes of uncertainty information are usually treated as time-independent or monotonic processes. The corresponding uncertainty analysis approaches are time independent. However, in this situation, the failure probabilities of performance can only be considered at the end of structure lifetime. To deal with the above challenge, an enhanced outcrossing rate method using the Kriging interpolation method is proposed in this study. The proposed method can utilize the correlation information between two design variables to predict the stress level and describe the time-dependent degeneration process. An uncertainty-based design and optimization problem of machine tool spindle is utilized to illustrate the effectiveness of the proposed strategy