SELECT s1.ID FROM binventory_ostemp s1 JOIN 
( SELECT Cust_FkId, ProcessID, MAX(Service_Duration) AS duration 
    FROM binventory_ostemp WHERE ProcessID='4d2d6068678bc' AND Overall_Rank IN 
    (
        SELECT MIN(Overall_Rank) FROM binventory_ostemp WHERE ProcessID='4d2d6068678bc' GROUP BY Cust_FkId
    )
    GROUP BY Cust_FkId
) AS s2 ON s1.Cust_FkId = s2.Cust_FkId AND s1.ProcessID=s2.ProcessID 
AND s1.Service_Duration=s2.duration AND s1.ProcessID='4d2d6068678bc' 
GROUP BY s1.Cust_FkId

It just goes away if there are more than 10K rows in that table. What it does is find rows for each customer who has min. of overall rank and in those max. of service duration for a given processid

Table Data

ID  Cust_FkId   Overall_Rank    Service_Duration  ProcessID
1       23         2                30             4d2d6068678bc
2       23         1                45             4d2d6068678bc
3       23         1                60             4d2d6068678bc
4       56         3                90             4d2d6068678bc
5       56         2                50             4d2d6068678bc
6       56         2                85             4d2d6068678bc