Bayesian　updating　plays　an　important　role　in　reducing　epistemic　uncertainty　and　making　more　reliable　predictions　of　the　structural　failure　probability.　In　this　context,　it　should　be　noted　that　the　posterior　failure　probability　conditional　on　the　updated　uncertain　parameters　becomes　a　random　variable　itself.　Hence,　characterizing　the　statistical　properties　of　the　posterior　failure　probability　is　important,　yet　challenging　task　for　risk-based　decision-making.　In　this　study,　an　efficient　framework　is　proposed　to　fully　characterize　the　statistical　properties　of　the　posterior　failure　probability.　The　framework　is　based　on　the　concept　of　Bayesian　updating　and　keeps　the　effect　of　aleatory　and　epistemic　uncertainty　separated.　To　improve　the　efficiency　of　the　proposed　framework,　a　weighted　sparse　grid　numerical　integration　is　suggested　to　evaluate　the　first　three　raw　moments　of　the　corresponding　posterior　reliability　index.　This　enables　the　reuse　of　evaluation　results　stemming　from　previous　analyses.　In　addition,　the　proposed　framework　employs　the　shifted　lognormal　distribution　to　approximate　the　probability　distribution　of　the　posterior　reliability　index,　from　which　the　mean,　quantile,　and　even　the　distribution　of　the　posterior　failure　probability　can　be　easily　obtained　in　closed　form.　Four　examples　illustrate　the　efficiency　and　accuracy　of　the　proposed　method,　and　results　generated　with　Markov　Chain　Monte　Carlo　combined　with　plain　Monte　Carlo　simulation　are　employed　as　a　reference.