To　translate　the　marginal　distributions　between　non-Gaussian　and　Gaussian　processes,　a　Hermite　polynomial　model　(HPM)　based　on　the　first　four　moments　was　developed　and　shown　to　have　high　flexibility　and　efficiency.　Due　to　monotonic　limitation,　there　are　some　processes　that　the　HPM　cannot　be　applied　to.　To　overcome　the　monotonic　limitation　an　alternative　methodology　has　been　developed,　in　which　the　need　to　identify　the　transition　points　between　different　models　makes　it　inconvenient　in　practice.　Furthermore,　the　alternative　methodology　applies　inappropriate　inverse　normal　transformation　expressions　for　negatively　skewed　processes.　Therefore,　a　straightforward　HPM　is　proposed　to　overcome　the　monotonic　limitation,　with　explicit　expressions　deduced　and　clear　applicable　ranges　provided.　The　applications　of　the　proposed　model　in　statistical　response　analysis　of　the　time-domain　solution　of　a　tension　leg　platform　and　the　assessment　of　the　reliability　of　a　hull　girder　for　floating,　production,　storage　and　offloading　(FPSO)　units　are　investigated　via　practical　examples,　which　demonstrate　that　the　proposed　model　can　be　efficiently　applied　to　marine　structures.