Database
[{X:[{Y:[{STATUS:"a"},{STATUS:"b"},{STATUS:"c"}]},{Y:[{STATUS:"a"},{STATUS:"b"},{STATUS:"c"}]}]}]
Query
db.collection.aggregate([{$project:{total_a:{$reduce:{input:"$X",initialValue:0,in:{$add:["$$value",{$size:{$filter:{input:"$$this.Y",as:"yy",cond:{$eq:["$$yy.STATUS","a"]}}}}]}}},total_X:{$size:"$X"}}}])