Reliability　assessment　of　ductile　frame　structures　in　a　systematic　manner　has　remained　a　challenging　issue　because　of　the　difficulties　in　searching　for　important　failure　modes　and　evaluating　the　system　probability　of　failure　stemmed　from　these　important　modes.　In　this　paper,　based　on　the　Box-Cox　transformation,　a　new　failure　mode　independent　performance　function　with　the　probability　distribution　of　weak　non-normality　is　proposed　for　the　system　reliability　assessment　of　ductile　frame　structures.　An　efficient　approach　is　then　developed　for　estimating　the　failure　probability　of　the　proposed　performance　function,　which　includes　two　steps:　first,　the　point-estimate　method　based　on　hybrid　dimension-reduction　integrated　with　structural　limit　analysis　is　developed　to　evaluate　the　first　four　central　moments　(i.e.,　mean,　standard　deviation,　skewness,　and　kurtosis)　of　the　proposed　performance　function;　next,　the　system　probability　of　failure　corresponding　to　the　proposed　performance　function　is　then　estimated　using　the　moment-based　reliability　method.　Three　numerical　examples　are　presented　to　demonstrate　the　efficiency　and　accuracy　of　the　proposed　method,　where　the　method　of　subset　simulation　is　employed　for　comparison.　It　can　be　concluded　that　the　developed　methodology　successfully　overcomes　the　two　difficulties　including　the　identification　of　important　failure　modes　and　the　evaluation　of　system　probability　of　failure　stemmed　from　these　important　modes　in　system　reliability　assessment　of　ductile　frame　structures.　©　The　Author(s)　2022.