This　paper　proposes　an　equivalent　expectation　evaluation　method　for　approximating　the　probability　distribution　of　performance　functions.　The　innovation　of　the　proposed　method　is　to　formulate　the　probability　distribution　of　the　performance　function　as　an　expectation　regardless　of　the　dimensionality　and　complexity　of　the　problem.　When　a　monotonic　inverse　function　(MIF)　of　the　performance　function　with　respect　to　a　certain　random　variable　can　be　obtained,　the　probability　distribution　can　be　exactly　formulated　as　an　expectation　related　to　the　distribution　of　this　variable　and　the　MIF.　While　if　such　a　MIF　does　not　exist　or　cannot　be　easily　obtained,　by　constructing　two　simple　auxiliary　functions　whose　MIF　can　be　obtained,　a　generalized　method　is　proposed　to　formulate　the　probability　distribution　of　the　performance　function　as　an　expectation　related　to　the　distribution　of　the　auxiliary　functions.　Then,　the　Sobol　sequence　and　point　estimate　method　are　employed　to　determine　the　expectation.　The　efficiency　and　accuracy　of　the　proposed　method　are　demonstrated　through　four　numerical　examples.　The　results　show　that　the　proposed　method　is　applicable　to　approximating　probability　distributions　of　both　static　and　dynamic　reliability　problems　involving　high-dimensional,　nonlinear,　or　implicit　performance　functions.