The　computational　efficiency　and　accuracy　of　the　time-dependent　reliability-based　robust　design　optimization　(TRBRDO)　directly　rely　on　the　capability　to　handle　the　time-dependent　reliability　analysis　(TRA).　Some　TRA　methods　use　ordinary　efficient　global　optimization　(EGO)　to　identify　the　extreme　samples,　and　the　Kriging　model　is　utilized　to　approximate　the　implicit　extreme　value　functions.　However,　the　significant　limitation　of　these　methods　lies　in　the　unavailability　for　the　parallelized　reliability　analysis,　resulting　from　the　point-to-point　nature,　which　indicates　the　computational　efficiency　can　be　further　improved.　To　construct　a　more　efficient　model　for　the　TRA,　this　paper　proposes　an　adaptive　Kriging　method,　i.e.,　integrated　parallel　efficient　global　optimization　(PEGO)　and　adaptive　Kriging-Monte　Carlo　simulation　(AK-MCS),　which　transforms　the　TRBRDO　problem　into　an　equivalent　time-independent　one.　The　proposed　adaptive　Kriging　method　was　proven　to　be　superior　to　existing　TRBRDO　methods　in　computing　efficiency　and　accuracy,　verified　by　the　performance　comparison　via　three　cases,　including　a　limit　state　function　with　only　a　time　parameter,　a　two-dimensional　function　generator,　and　an　engineering　application.