To　improve　rescue　efficiency,　a　multi-function　rescue　attachment　with　tonging,　shearing　and　grasping　functions　was　designed　by　the　authors　in　a　previous　study.　In　this　paper,　the　reliability　and　reliability　sensitivity　of　this　rescue　attachment　are　researched.　Three　rescue　attachment　failure　modes　are　analyzed　and　limit　state　equations　are　established　for　the　three　failure　modes.　To　consider　the　complex　and　nonlinear　correlations　among　these　failure　modes,　a　method　to　analyze　the　reliability　and　sensitivity　to　reliability　of　the　failure　modes　based　on　a　hybrid　copula　model　is　proposed.　The　Clayton　copula,　Gumbel　copula　and　Frank　copula,　which　exhibit　upper　tail　dependence,　lower　tail　dependence,　and　upper　and　lower　tail　independence,　respectively,　are　selected　to　construct　the　hybrid　copula　model　to　describe　the　complex　correlations　among　multiple　failure　modes.　The　weight　coefficients　and　parameters　of　the　hybrid　copula　model　are　then　estimated　using　the　Bayesian　model　weighted　average　method　and　the　minimum　square　deviation　criterion.　A　method　to　calculate　the　sensitivity　of　the　failure　correlations　to　the　reliability　is　then　deduced　using　the　moment　method　to　improve　the　computational　efficiency.　Two　examples　show　that　the　proposed　method　can　improve　computational　efficiency　significantly　and　the　calculation　results　were　consistent　with　those　realized　using　the　Monte　Carlo　(MC)　method,　but　required　fewer　samples.　Finally,　the　reliability　and　reliability　sensitivity　of　the　rescue　attachment　are　analyzed　using　the　proposed　method　and　MC　method.　The　effectiveness　and　efficiency　of　the　proposed　method　are　proved,　and　strategies　to　improve　the　rescue　attachment’s　reliability　are　determined.　©　2021,　The　Brazilian　Society　of　Mechanical　Sciences　and　Engineering.