Machining　accuracy　retainability　is　considered　to　be　one　of　the　most　important　aspects　in　the　process　of　performance　evaluation　and　optimization　design　of　the　machine　tools.　Reliability　based　design　optimization　(RBDO)　and　robust　design　optimization　(RDO)　are　the　tools　that　search　for　safe　structural　systems　with　minimal　variability　of　response　when　subjected　to　uncertainties　in　design　parameters.　The　aim　of　this　paper　is　to　propose　an　approach　that　simultaneously　considers　reliability　and　robustness　to　allocate　geometric　accuracy　of　components　for　improving　machining　accuracy　retainability　under　certain　design　requirements.　Based　on　homogenous　transformation　matrices　(HTMs),　a　comprehensive　volumetric　model　explaining　how　individual　errors　in　the　components　of　a　machine　affect　its　volumetric　accuracy　(the　coupling　relationship)　was　established.　By　applying　high-order　moment　standardization　technique　(HOMST),　reliability　and　sensitivity　with　single　failure　mode　were　obtained　and　then　the　reliability　model　and　the　sensitivity　model　with　multiple　failure　modes　were　developed　and　common　methods　such　as　Narrow　bounds,　AFOSM　and　Monte　Carlo　were　used　for　verification　and　comparison.　Meanwhile,　a　cost　model　taking　manufacturing　cost　and　present　worth　of　expected　quality　loss　into　consideration　was　introduced.　By　taking　the　minimum　possibility　of　failure　and　cost　of　machine　tools　as　criterions　and　taking　the　reliability　of　machine　tools　as　constraint　of　optimizing　the　basic　parameters　of　machine　tools,　an　approach　to　optimize　the　machining　accuracy　retainability　of　multi-axis　NC　machine　tool　based　on　robust　design　was　developed　and　an　example　of　improving　the　machining　accuracy　retainability　for　a　five-axis　NC　machine　tool　was　used　to　demonstrate　the　effectiveness　of　this　approach.　This　study　implies　that　it　is　possible　to　obtain　the　relationships　between　geometric　errors　and　specify　the　accuracy　grades　of　main　feeding　components　of　mechanical　assemblies.　(C)　2015　Elsevier　Inc.　All　rights　reserved.