Traditional　reliability　analysis　aims　to　compute　the　failure　probability　based　on　probability　distribution　functions,　which　are　constructed　using　the　moments　of　random　parameters.　In　practice,　however,　appropriate　samples　may　be　insufficient　to　obtain　deterministic　values　of　the　moments　of　all　random　variables　and　the　exact　value　of　failure　probability　cannot　be　obtained.　To　be　consistent　with　the　reality,　the　uncertainties　in　moments　can　be　measured　as　interval　variables,　and　then　the　bounds　of　failure　probability　should　be　evaluated.　In　this　study,　an　idealized　case　is　considered,　where　there　is　at　most　one　imprecise　moment　associated　with　any　given　input　random　variable.　A　third　moment　method　is　proposed　with　uncertain　moments　measured　as　interval　variables,　and　is　named　as　TMI　method.　The　proposed　TMI　method　is　straightforward　including　only　four　steps.　Firstly,　the　derivative　of　performance　function　to　random　variables　having　uncertain　moments　is　calculated,　with　the　random　variables　set　to　be　their　mean　values.　Secondly,　the　values　of　uncertain　moments　for　computing　the　bounds　of　failure　probability　are　determined.　Then,　with　inverse　normal　transformation　defined　based　on　the　moments,　the　performance　function　at　the　bounds　in　Gaussian　space　is　directly　constructed.　Finally,　bounds　of　failure　probability　can　be　evaluated　by　two　times　of　classical　reliability　analysis　corresponding　to　the　constructed　performance　functions.　The　application　of　TMI　method　is　validated　by　numerical　examples,　including　high-dimensional　and　strong　nonlinear　problems.　©　2024　Elsevier　Ltd