Phased-mission　systems　widely　exist　in　many　real-world　systems　such　as　communication　networks,　aerospace　and　unmanned　aerial　vehicles.　The　reliability　modeling　and　analysis　of　phased-mission　systems　is　highly　important　due　to　their　indispensable　roles　in　the　society.　Reliability　analysis　of　a　phased-mission　system　is　challenging　because　of　the　statistical　dependencies　between　different　phases　and　the　dynamic　behaviors　of　system　components.　This　research　considers　a　phased-mission　system　with　a　common　bus　and　warm　standby　elements.　Each　unit　of　the　phased-mission　system　consists　of　n　binary-state　nonrepairable　elements　that　are　configured　as　a　1-out-of-n:　G　warm　standby　system.　A　recursive　algorithm　is　proposed　to　determine　the　performance　of　the　stochastic　process　with　arbitrary　time-to-failure　distributions.　A　reliability　evaluation　algorithm　based　on　the　universal　generating　function　is　proposed　to　analyze　the　average　instantaneous　availability　of　the　considered　system.　We　further　study　the　optimal　system　design　problem　that　aims　to　find　the　optimal　elements　allocation　as　well　as　the　optimal　activation　sequence　to　maximize　the　average　instantaneous　availability.　A　case　study　of　a　supervisory　control　and　data　acquisition　system　is　presented　to　illustrate　the　application　of　the　proposed　model　and　algorithms.