In　the　reliability　literature,　studies　that　jointly　investigate　maintenance　and　production　are　typically　restricted　to　one　failure　mode　and　fail　to　address　the　case　where　multiple　failure　modes　may　exist.　This　study　investigates　the　problem　of　joint　optimization　of　lot　sizing　and　maintenance　policy　for　a　multi-product　production　system　subject　to　two　failure　modes.　The　failure　of　the　first　mode　is　a　soft　failure　that　occurs　after　defects　arrive.　The　failure　of　the　second　mode　is　a　hard　failure　that　occurs　without　any　early　warning　signals.　Products　are　sequentially　produced　by　the　system　and　a　complete　run　of　all　products　forms　a　production　cycle.　The　system　needs　to　be　reset　up　before　producing　a　different　product.　Both　the　production　cycle　and　the　time　of　set-up　depend　on　the　lot　sizes　of　products.　Models　are　proposed　for　two　maintenance　policies:　1)　arranging　the　maintenance　during　the　set-up　at　the　end　of　each　production　cycle;　2)　arranging　the　maintenance　during　each　of　set-ups.　The　expected　profit　per　unit　time　is　formulated　to　obtain　the　optimal　lot　sizing　and　maintenance　policy.　Some　properties　of　the　proposed　models　are　provided　and　they　show　that　the　optimal　lot　sizing　and　maintenance　policy　can　be　obtained　under　certain　conditions.　Case　studies　and　sensitivity　analyses　are　presented　to　illustrate　the　proposed　models　of　two　maintenance　policies.　The　results　show　that　the　manufacturer　will　gain　the　most　profit　if　the　optimal　lot　sizing　and　maintenance　policy　are　adopted.　The　results　of　comparing　both　maintenance　policies　reveal　that　the　excessive　maintenance　is　not　cost-effective.　The　sensitivity　analyses　illustrate　that　reducing　the　cost　due　to　failures　and　improving　system　reliability　are　effective　ways　to　increase　the　expected　profit　per　time　unit.