The　robustness　of　a　schedule　is　an　important　problem　in　practice.　In　this　paper　it　is　studied　in　the　angle　that　the　optimal　schedules　do　not　change.　Firstly　the　interval　perturbation　robustness　of　an　optimal　schedule　is　defined,　that　is　the　property　that　an　optimal　schedule　keeps　the　same　when　some　of　the　parameters　in　the　scheduling　problem　vary　in　some　intervals.　Then　the　interval　perturbation　robustness　of　an　optimal　schedule　for　single　machine　discounted　total　weighted　completion　time　is　studied.　Form　a　lemma　that　gives　the　relationship　between　the　order　of　r　parameters　and　the　overlaps　between　each　two　of　the　intervals　in　which　these　parameters　vary,　the　results　in　this　paper　are　proved.　The　results　are　three　if　and　only　if　conditions　under　which　an　optimal　schedule　is　of　interval　perturbation　robustness.　These　results　relate　to　the　optimality　of　a　schedule　at　some　of　the　vertices　of　a　hyperrectangle　of　r　dimension　consisting　of　the　varying　parameters.　Some　examples　that　show　how　to　use　these　results　are　given.