This　contribution　introduces　a　novel　framework　for　the　first　excursion　probability　sensitivity　estimation,　applicable　to　linear　dynamic　systems　subject　to　a　Gaussian　excitation.　The　proposed　methodology　is　based　on　Domain　Decomposition　method,　and　the　sensitivity　estimator　is　calculated　as　the　partial　derivative　of　the　first　excursion　probability　with　respect　to　a　design　parameter,　such　as　the　geometrical　dimensions　of　the　system.　The　linearity　of　the　system　plays　a　key　role　in　building　an　efficient　estimator.　Domain　Decomposition　Method　exploits　this　feature　by　exploring　the　failure　domain　in　a　very　convenient　way　due　to　its　special　structure,　characterized　by　the　union　of　a　large　number　of　elementary　linear　failure　domains.　This　approach　allows　the　sensitivity　estimator　to　be　derived　as　a　byproduct　of　the　first　excursion　probability　estimator.　The　effectiveness　of　this　technique　is　demonstrated　through　a　numerical　example　involving　a　large-scale　model.　©　2024　Proceedings　of　ISMA　2024　-　International　Conference　on　Noise　and　Vibration　Engineering　and　USD　2024　-　International　Conference　on　Uncertainty　in　Structural　Dynamics.　All　rights　reserved.