In　the　safety　assessment　of　structures,　the　simultaneous　consideration　of　aleatory　uncertainty　and　epistemic　uncertainty　(generally　represented　by　random　variables　and　interval　variables,　respectively)　is　increasingly　recognized.　From　the　angle　of　the　tradeoff　of　efficiency　and　accuracy,　finding　a　solution　for　this　problem　remains　challengeable.　Motivated　by　this,　this　paper　proposes　a　novel　random-interval　reliability　analysis　method,　called　ALK-TSS-HRA,　by　combining　active　learning　Kriging　(ALK)　and　two-phase　subset　simulation　(TSS).　Based　on　the　idea　that　small　failure　probability　can　be　converted　into　the　product　of　a　series　of　large　failure　probabilities,　the　proposed　TSS　evaluates　the　upper　and　lower　bounds　of　failure　probability　in　two　phases.　The　estimation　of　lower　bound　in　the　second　phase　makes　full　use　of　the　upper　bound　and　failure　samples　in　the　first　phase,　so　as　to　achieve　high　efficiency.　Furthermore,　Kriging　metamodel　is　used　to　substitute　the　actual　limit　state　function　in　TSS　to　lower　the　computational　overhead.　In　ALK-TSS-HRA,　the　training　points　mostly　contributing　to　the　estimations　of　the　upper　and　lower　bounds　of　failure　probability　are　identified　in　two　phases　of　TSS,　respectively.　Then,　the　Kriging　metamodel　is　sequentially　updated　in　a　series　of　small　intermediate　sample　pools,　which　greatly　shortens　the　training　time.　The　computational　efficiency　and　accuracy　of　the　proposed　method　is　demonstrated　by　its　comparison　with　the　state-of-the-art　methods　through　four　representative　examples.　©　2024　Institution　of　Structural　Engineers