Even　well-designed　software　systems　suffer　from　chronic　performance　degradation,　also　known　as　＂software　aging＂,　due　to　internal　(e.g.,　software　bugs)　or　external　(e.g.,　resource　exhaustion)　impairments.　These　chronic　problems　often　fly　under　the　radar　of　software　monitoring　systems　before　causing　severe　impacts　(e.g.,　system　failures).　Therefore,　it　is　a　challenging　issue　how　to　timely　predict　the　occurrence　of　failures　caused　by　these　problems.　Unfortunately,　the　effectiveness　of　prior　approaches　are　far　from　satisfactory　due　to　the　insufficiency　of　aging　indicators　adopted　by　them.　To　accurately　predict　failures　caused　by　software　aging　which　are　named　as　Aging-Related　Failure　(ARFs),　this　paper　presents　a　novel　entropy-based　aging　indicator,　namely　Multidimensional　Multi-scale　Entropy　(MMSE)　which　leverages　the　complexity　embedded　in　runtime　performance　metrics　to　indicate　software　aging.　To　the　best　of　our　knowledge,　this　is　the　first　time　to　leverage　entropy　to　predict　ARFs.　Based　upon　MMSE,　we　implement　three　failure　prediction　approaches　encapsulated　in　a　proof-of-concept　prototype　named　ARF-Predictor.　The　experimental　evaluations　in　a　Video　on　Demand　(VoD)　system,　and　in　a　real-world　production　system,　AntVision,　show　that　ARF-Predictor　can　predict　ARFs　with　a　very　high　accuracy　and　a　low　Ahead-Time-To-Failure　(ATTF).　Compared　to　previous　approaches,　ARF-Predictor　improves　the　prediction　accuracy　by　about　5　times　and　reduces　ATTF　even　by　3　orders　of　magnitude.　In　addition,　ARF-Predictor　is　light-weight　enough　to　satisfy　the　real-time　requirement.