Time-dependent　positional　reliability,　mathematically　defined　as　the　probability　of　the　positional　error　falling　inside　a　specified　safe　boundary　over　a　time　interval,　is　of　importance　for　robotic　manipulators.　This　work　proposes　an　enhanced　moment-based　approach　integrating　the　Lie-group　theory,　series　expansion　simulation,　sparse　grid　Gauss-Hermite　integration　technique　and　chi-square　approximation　to　attacking　this　problem.　The　novelties　of　this　work　lie　in　two　points.　On　the　one　hand,　different　from　previous　methods　that　compute　the　first　to　fourth　order　moments　directly　using　the　original　limit-state　function,　the　proposed　method　takes　advantage　of　the　Lie　group　theory,　PCE　and　EOLE　to　transform　the　original　limit-state　error　function　into　a　simple　surrogate　one　for　moment　calculation,　which　helps　to　get　rid　of　repeatedly　calling　the　original　error　function　and　therefore　results　in　a　great　enhancement　in　efficiency.　On　the　other　hand,　the　proposed　method　first　introduces　the　non-central　chi-square　approximation　to　rebuild　the　extreme　value　distribution　of　the　positional　error,　by　which　the　accuracy　of　time-dependent　positional　reliability　analysis　is　highly　enhanced.　Finally,　a　6-DOF　robotic　manipulator　is　showcased　to　demonstrate　the　effectiveness　and　advantages　of　the　proposed　approach.　©　2020