Evaluating　the　large　reliability　index　of　an　implicit　and　nonlinear　performance　function　(PF)　is　still　a　challenging　problem　in　practical　engineering.　To　overcome　this　problem,　an　efficient　method　by　using　multiple　techniques　is　proposed.　A　strategy　is　proposed　to　select　the　optimal　transformation　parameter　(OTP)　that　makes　the　transformed　PF　approximately　normally　distributed.　This　strategy　is　established　based　on　the　power　transformation　family　including　Box-Cox　and　dual　power　transformation,　in　which　three　formulations,　i.e.,　maximum　likelihood　estimation,　Jarque-Bera　test,　and　absolute　skewness　minimization　criterion　are　first　introduced　to　estimate　the　transformation　parameters.　Further,　the　selective　factors　corresponding　to　the　three　different　formulations　can　be　estimated　based　on　the　minimum　distance　between　the　pair　of　the　skewness　and　kurtosis　of　the　transformed　PF　and　that　of　a　normal　random　variable,　where　the　first　four　moments　of　the　transformed　PF　are　evaluated　from　the　high-order　unscented　transformation.　Then,　the　OTP　can　be　chosen　as　the　one　with　minimum　selective　factor.　Eventually,　the　reliability　index　can　be　obtained　based　on　the　first　four　moments　of　the　transformed　PF　and　the　cubic　normal　distribution.　The　accuracy　and　efficiency　of　the　proposed　method　are　demonstrated　through　four　numerical　examples　with　nonnormal,　nonlinear　and　implicit　PFs.