Kinematic　reliability　is　an　essential　index　assessing　the　work　performance　of　robotic　manipulators.　In　general,　the　kinematic　reliability　of　robotic　manipulators　is　defined　as　the　probability　of　the　pose　or　position　error　falling　into　a　specified　tolerant　region.　Therefore,　this　work　proposes　an　efficient　method　to　conduct　kinematic　reliability　analysis　for　robotic　manipulators　under　rectangular　and　spherical　allowable　safe　boundaries　in　terms　of　dimension　and　input　uncertainties.　First,　based　on　the　Baker-Campbell-Hausdorff　formula　and　Lie　group　theory,　the　mean　and　covariance　matrix　of　the　distribution　of　the　pose　error　are　analytically　determined.　Then,　the　expectation　propagation　of　the　multivariate　Gaussian　and　saddlepoint　approximation　method　are　employed　to　calculate　the　probabilities　of　kinematic　reliability　under　the　rectangular　and　spherical　safe　boundaries,　respectively.　The　proposed　method　takes　into　account　the　boundness　of　the　random　error　variable　and　is　available　for　arbitrarily　distributed　errors.　Finally,　a　spatial　six　degrees-of-freedom　industrial　robot　is　used　as　an　example　to　demonstrate　the　effectiveness　of　the　proposed　method　by　comparison　with　other　methods.　The　comparison　results　indicate　that　the　proposed　method　has　higher　accuracy　and　efficiency.