The　inventory　cost　of　stocking　spare　parts　is　a　nonnegligible　expenditure　of　providing　after-sales　service　for　the　manufacturers　making　capital-intensive　products,　such　as　electric　vehicles.　Especially,　for　warranty　repair　service,　it　is　important　to　manage　the　spare　stock　appropriately　to　satisfy　the　warranty　claims　of　customers　as　well　as　reduce　the　associated　inventory　costs.　In　this　paper,　we　investigate　the　spare　parts　inventory　issue　related　to　a　critical　component　for　under-warranty　units　of　a　product.　In　particular,　under　the　free-replacement　warranty　policy,　failed　component　will　be　replaced　by　a　new　one　by　consuming　the　spare　stock.　According　to　the　field　claim　data,　we　find　that　the　general　trend　of　warranty　claims　is　nonstationary,　which　will　be　affected　by　the　product　sales　and　under-warranty　failures.　Thus,　we　first　propose　a　model　to　forecast　the　time-varying　warranty　repair　demand　by　explicitly　considering　the　randomness　from　two　major　sources,　that　is,　product　sales　and　under-warranty　failures.　Under　the　assumptions　of　Poisson　sales　process　and　exponential　failure　distribution,　the　closed-form　expressions　of　mean　and　variance　of　cumulative　warranty　repair　demand　over　time　are　obtained.　Because　the　number　of　warranty　claims　in　each　period　is　a　one-time　data,　the　associated　distribution　information　is　unavailable.　Then,　based　on　the　properties　of　the　demand　statistics,　we　derived　a　worst-case　upper　bound　for　the　associated　inventory　cost　and　formulate　a　three-phase　finite-horizon　spare　parts　inventory　model,　which　can　be　used　to　appropriately　address　the　time-varying　warranty　claims.　Finally,　numerical　experiments　are　conducted　to　investigate　the　key　parameters　affecting　the　optimal　decisions　where　a　case　study　based　on　real　data　is　presented.