With　the　ever　increasing　demand　of　higher　machining　accuracies,　the　machining　accuracy　reliability　has　evolved　into　an　indicator　to　evaluate　the　performance　of　a　machine　tool.　Consequentially,　methods　for　improving　the　machining　accuracy　reliability　have　become　the　focus　of　attention　for　both　manufacturers　and　users.　Generally,　the　intercoupling　geometric　errors　are　the　main　cause　which　may　lead　to　a　reduction　of　the　machining　accuracy　of　machine　tools.　In　this　paper,　the　machining　accuracy　reliability　is　defined　as　the　ability　of　a　machine　tool　to　perform　at　its　specked　machining　accuracy　under　the　stated　conditions　for　a　given　period　of　time,　and　a　new　approach　for　analyzing　the　machining　accuracy　reliability　of　machine　tools　based　on　fast　Markov　chain　simulations　is　proposed.　Using　this　method,　seven　different　failure　modes　could　be　determined　for　a　machine　tool.　An　analysis　of　the　machining　accuracy　reliability　sensitivity　was　performed　based　on　solving　the　integral　of　the　failure　probability　of　the　machine　tool,　and　the　key　geometric　errors　which　most　strongly　affect　the　machining　accuracy　reliability　were　identified.　Finally,　in　this　study,　a　4-axis　machine　tool　was　selected　as　an　example　to　experimentally　validate　the　effectiveness　of　the　proposed　method.