Inspection　is　usually　carried　out　periodically　to　update　a　system　state　such　that　the　optimal　maintenance　policy　can　be　determined.　In　order　to　obtain　the　best　inspection　and　maintenance　policy,　existing　research　is　focused　on　improving　the　modeling　accuracy　of　the　system　failure　process.　Little　work　has　been　devoted　to　making　full　use　of　the　system　idle　time,　which　is　known　as　the　production　wait　in　production　systems.　In　this　research,　the　failure　process　of　a　single-unit　system　is　modeled　in　three　stages　with　consideration　of　its　production　wait　time.　The　objective　of　minimizing　the　long-run　average　maintenance　cost　per　unit　time　is　achieved　by　finding　the　optimal　length　of　the　periodic　inspection　interval　and　renewal　age　for　this　single-unit　system.　By　comparing　this　model　with　two　two-stage　inspection　models,　the　numerical　study　of　a　real　steelmaking　converter　confirms　both　the　accuracy　and　effectiveness　of　the　proposed　inspection　and　maintenance　model.　Furthermore,　the　sensitivity　analysis　of　different　parameters　is　conducted　to　explore　the　optimal　choice　of　maintenance　strategy　for　different　cost　parameters　and　degradation　parameters.　The　analysis　provides　useful　management　insights　for　decision-makers.