Evaluating　the　statistical　moments　of　performance　functions　from　the　perspective　of　balancing　accuracy　and　efficiency　remains　a　challenge.　This　paper　proposes　an　efficient　algorithm　for　evaluating　the　statistical　moments　of　performance　functions.　The　main　procedure　of　the　proposed　method　consists　of　three　steps.　First,　based　on　the　bivariate　dimension-reduction　method,　the　performance　function　is　approximated　by　a　summation　of　one-dimensional　and　two-dimensional　functions.　Next,　according　to　the　criterion　of　delineating　the　existence　of　cross　terms,　the　two-dimensional　functions　are　decomposed　as　functions　including　and　excluding　cross　terms.　Third,　the　one-dimensional　point　estimate　method　is　used　to　evaluate　the　statistical　moments　of　the　one-dimensional　functions　and　the　two-dimensional　functions　without　cross　terms,　whereas　the　two-dimensional　sparse　grid　stochastic　collocation　method　is　applied　to　estimate　the　statistical　moments　of　the　two-dimensional　functions　with　cross　terms.　Several　numerical　examples　are　presented　to　illustrate　the　efficiency,　accuracy,　and　applicability　of　the　proposed　method.　The　results　demonstrate　that　the　proposed　method　achieves　a　good　balance　between　accuracy　and　efficiency　and　provides　a　useful　tool　for　evaluating　the　statistical　moments　of　performance　functions.