The　localization　of　outer　raceway　defect　plays　a　significant　role　in　malfunction　elimination,　failure　cause　analysis　as　well　as　the　residual　life　prediction　of　ball　bearings.　Based　on　the　nonlinear　dynamic　model　for　a　ball　bearing　and　the　outer　raceway　defect　model　considering　the　ball　finite　size,　this　article　employs　the　detailed　mathematical　derivation　and　theoretical　analysis　of　the　load　distribution　for　the　bearing　system　with　an　outer　raceway　defect　located　at　the　different　angular　positions.　Therefore,　the　essential　mechanism　of　the　approximate　linear　relationship　between　the　proposed　indices,　namely　horizontal-vertical　synchronized　Peak　(HVSPeak)　and　horizontal-vertical　synchronized　RMS　(HVSRMS),　and　the　defect　angular　position　is　explained.　More　importantly,　it　is　theoretically　demonstrated　that　HVSRMS　is　approximately　a　cotangent　function　with　the　defect　angular　position　as　the　only　variable,　which　indicates　that　the　index　has　excellent　anti-interference　and　practicability.　In　addition,　the　superiority　and　necessity　of　the　HVSRMS　index　can　be　seen　when　compared　to　HVSPeak,　RMS,　SampEn　and　Lemple-Ziv.　It　is　validated　through　simulation　and　experiment　results　that　HVSRMS　index　can　efficiently　diagnose　the　angular　position　of　outer　raceway　defect.　Finally,　the　signal　denoising　methods　for　HVSRMS　are　compared　and　studied,　which　indicates　the　direction　for　subsequent　research.