The　usual　approach　to　time-variant　reliability　problems　is　PHI2　method,　which　defines　the　outcrossing　rate　as　a　two-component　parallel　system　problem　and　calculates　it　through　a　two-dimensional　numerical　integration.　To　improve　the　computational　efficiency,　an　explicit　model　of　outcrossing　rate　is　proposed　in　this　study,　which　is　referred　to　as　EPHI2.　Based　on　the　proposed　explicit　model,　EPHI2　method　avoids　the　numerical　integration　required　in　PHI2　method.　Comparison　between　the　outcrossing　rates　obtained　by　PHI2　and　EPHI2　methods　was　conducted,　and　EPHI2　method　was　proved　to　have　enough　accuracy　for　calculating　outcrossing　rates.　The　application　of　EPHI2　method　for　time-variant　reliability　analysis　was　investigated　through　three　numerical　examples.　It　is　found　that　the　proposed　EPHI2　method　is　more　efficient　than　PHI2　method　in　time-variant　reliability　analysis,　with　the　results　nearly　the　same.　(C)　2021　American　Society　of　Civil　Engineers.