This　paper　studies　the　reliability　of　a　distributed　computing　system　where　the　task　on　a　computer　may　be　aborted　if　it　is　still　not　finished　until　a　time　threshold.　The　mission　is　regarded　as　successful　if　all　these　tasks　are　completed　by　at　least　one　computer　before　a　pre-specified　time.　An　abort　policy　model　is　proposed　and　a　multi-valued　decision　diagram　approach　is　adopted　to　evaluate　the　system　reliability　for　any　given　abort　policy.　A　numerical　example　is　provided　to　illustrate　the　applications.