Most　theoretical　analysis　for　lifetime　distribution　explains　origins　of　specific　distribution　based　on　independent　failure.　We　develop　one　unified　framework　encompassing　different　kinds　of　lifetime　distribution　for　failure　coupling　system.　For　typical　complex　networks,　we　found　that　three　types　of　system　lifetime　distributions　are　emerged　shaped　by　system　size　and　failure　coupling　strength.　When　the　failure　coupling　strength　ϕ　dominates,　systems　exhibit　a　cascade　failure　mode,　the　system　lifetime　following　an　exponential　distribution　as　series　systems　due　to　long-range　correlation.　When　the　system　size　N　dominates,　systems　exhibit　wear-out　failure　mode,　the　system　lifetime　following　the　Gompertz　model　as　parallel　systems　due　to　short-range　correlation.　When　N　and　ϕ　have　comparable　impact　on　systems,　system　lifetime　follows　a　modified　Weibull　distribution.　We　find　the　critical　failure　coupling　strength　and　critical　system　size　which　are　helpful　to　identify　the　failure　mode　switch　point.　We　provide　rigorous　theoretical　analysis　for　emerged　lifetime　distribution.　We　reveal　the　microscopic　mechanism　of　system　lifetime　distribution　switch　pattern　by　analyzing　the　competence　between　correlation　length　and　network　diameter.　Finally,　we　verify　our　conclusions　in　real　networks.　Our　study　will　help　to　understand　the　lifetime　origin　of　complex　systems　and　design　highly　reliable　systems.　©　2024　Elsevier　Ltd