To　improve　the　performance　of　a　conventional　rescue　equipment,　we　designed　a　novel　multi-functional　rescue　end-effector　comprising　a　separation　mechanism　and　a　grasping　mechanism.　The　failure　causes　of　the　separation　mechanism　are　analyzed,　and　three　main　failure　modes　are　determined.　Meanwhile,　their　performance　functions　are　established　as　well.　To　solve　the　complex　correlations　among　multiple　failure　modes,　a　novel　mixed　copula　function　that　can　capture　the　upper　and　lower　tail　dependencies　simultaneously　is　proposed,　which　comprises　the　Gumbel　copula　and　the　Clayton　copula.　Further,　a　novel　procedure　that　adopts　the　non-parametric　kernel　density　estimation　(NKDE)　technique　to　estimate　the　probability　density　function　(PDF)　and　the　cumulative　distribution　function　(CDF)　for　each　performance　function　of　the　separation　mechanism　is　proposed.　The　parameters　of　the　mixed　copula　function　are　estimated　using　the　method　of　maximum　likelihood　estimation.　Subsequently,　to　further　study　the　separation　mechanism＇s　reliability　during　working,　a　time-variant　parameter　estimation　method　is　introduced　to　build　the　time-variant　mixed　copula　function.　Finally,　both　the　reliability　and　time-variant　reliability　of　the　separation　mechanism　are　analyzed　via　the　proposed　integral　methods.　Comparisons　with　other　analysis　schemes　show　that　the　proposed　integral　method　is　not　only　effective　but　also　efficient　in　analyzing　the　reliability　of　our　target　mechanism.