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Reliability represents safety level in industry practice and may variant due to time-variant operation condition and components deterioration throughout a product life-cycle. Thus, the capability to perform time-variant reliability analysis is of vital importance in practical engineering applications. This paper presents a new approach, referred to as nested extreme response surface (NERS), that can efficiently tackle time dependency issue in time-variant reliability analysis and enable to solve such problem by easily integrating with advanced time-independent tools. The key of the NERS approach is to build a nested response surface of time corresponding to the extreme value of the limit state function by employing Kriging model. To obtain the data for the Kriging model, the efficient global optimization technique is integrated with the NERS to extract the extreme time responses of the limit state function for any given …