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This paper proposes two computation schemes for efficient evaluation of sets of reliability analyses associated with different time intervals. The first approach is based on sequential solving the reliability analyses starting from the last time interval. It enables to use the solution of a time interval as a starting point and to efficiently solve the reliability problem of preceding time intervals. Its implementation combined with Subset Simulation (SuS) and Sequential Importance Sampling (SIS) is presented. The second proposed approach is centered around reformulating the limit state function in a way that the time to failure can be described. This allows to efficiently obtain the estimates of failure probabilities and corresponding time intervals by one run of SuS. The numerical verification demonstrates that the proposed methods are capable of obtaining accurate estimates of lifetime reliability with a substantially reduced computational cost. ; The research leading to these results has received funding from the SAFEPEC project under the European Union's FP7 programme.