Time-dependent　reliability　analysis　of　deteriorating　structures　is　significant　in　their　performance　assessment　and　maintenance.　Various　methodologies　have　been　used　by　researchers　to　predict　the　time-dependent　reliability　of　structures.　However,　it　is　still　a　challenge　to　estimate　the　small　time-dependent　failure　probability　in　high　dimensions.　In　the　present　study,　based　on　subset　simulation　an　adaptive　stochastic　simulation　procedure　is　proposed　considering　the　stochastic　nature　of　the　occurrence　of　time-dependent　random　variables.　Moreover,　a　modified　Metropolis-Hastings　algorithm　is　developed　to　reduce　repeated　trajectories　and　suit　the　property　of　time-dependent　reliability　problem.　Fourth-moment　transformation　is　utilized　in　the　study　for　without　the　exclusion　of　random　variables　with　unknown　probability　distributions.　The　proposed　method　is　illustrated　by　a　cantilever　tube　subjected　to　external　forces　and　torsion.　The　methodology　can　be　used　as　a　tool　for　structural　engineers　and　asset　managers　to　assess　small　time-dependent　failure　probability　of　a　deteriorating　structure　in　high　dimensions　and　make　decisions　with　regard　to　its　maintenance　and　rehabilitation.　©　13th　International　Conference　on　Applications　of　Statistics　and　Probability　in　Civil　Engineering,　ICASP　2019.　All　rights　reserved.