The objective of this paper is to investigate system reliability methods for time-variant reliability analysis. The main challenge in time-variant reliability analysis is dealing with low probabilities of failure while computationally expensive performance functions are involved. Time-variant problems are often simplified by discretizing time intervals. This enables one to transform the initial problem to a system problem. System reliability methods can therefore be used to address time-variant reliability problems. AK-SYS is an efficient system reliability method which can be applied when costly-to-evaluate performance functions are considered. Application of this method for time-variant reliability problems is introduced in this paper that is supported with two academic examples from literature.