In　this　paper,　a　new　analytical　formula　is　proposed　to　determine　the　mean　outcrossing　rate　of　nonstationary　non-Gaussian　performance　functions.　The　performance　function　is　firstly　transformed　into　a　standard　Gaussian　process　using　its　first　four　moments　and　autocorrelation　coefficient　function,　and　the　mean　outcrossing　rate　of　the　time-variant　performance　function　is　then　derived　from　the　transformed　standard　Gaussian　process　and　the　cumulative　distribution　function　of　the　correlated　bivariate　standard　normal　random　variable.　Based　on　the　proposed　mean　outcrossing　rate,　an　efficient　methodology　is　then　developed　to　evaluate　the　time-dependent　structural　failure　probability　of　nonstationary　non-Gaussian　performance　functions　under　the　assumption　that　the　outcrossing　event　(i.e.,　structural　failure)　is　modeled　as　a　Poisson　process.　Several　numerical　examples　are　presented　to　demonstrate　the　accuracy　and　efficiency　of　the　proposed　method.　It　can　be　concluded　that　the　proposed　method　provides　an　efficient　and　useful　tool　for　time-dependent　structural　reliability　assessment　in　engineering　applications.　(c)　2020　American　Society　of　Civil　Engineers.