Robust　design　(RD)　is　an　important　method　because　it　can　reduce　the　variation　of　products　or　processes　and　improve　their　performances　such　as　static　and　dynamic　quality　characteristics　at　a　low　cost.　In　order　to　obtain　an　efficient　and　universal　RD　solution,　a　novel　analytical　RD　methodology　is　proposed　based　on　axiomatic　design　principles.　The　covariance　matrix　of　multiple　functional　requirements　(FRs)　that　can　reflect　dependency　relationship　is　obtained　via　the　Talyor　series　expansion.　Evaluation　mechanism　based　on　information　axiom　is　introduced　to　select　the　better　design　scheme　gained　with　different　robust　optimization　models.　The　distinct　characteristics　of　the　proposed　method　are　the　implementation　by　matrix　differential,　and　the　ability　that　can　deal　with　multiple　FR　optimization　simultaneously.　An　RD　optimization　of　a　five　roller　coating　head　is　illustrated.　The　results　show　that　the　proposed　method　can　optimize　the　design　parameters　which　meet　the　multiple　FRs.　Copyright　(C)　2013　John　Wiley　&　Sons,　Ltd.