Hi Stefan,
Thanks for the reply and I really appreciate your time.
I should take this oppurtunity to thank you 
. I read very good blogs written by you and also I gain lot of knowledge by reading your suggestions in SDN blogs.
Yes, stefan as you mentioned that was my first method. I took the database export directly. I just logged in to my source system and just took the database Instance export to my local file system only to fasten the process. As my sandbox is of 4TB it took the downtime of 9 hours in total. The dump I got is 400GB in my ABAP directory of the export location.
In method 2. I approach of splitting my top size tables which I got from DB02 or ST04. I manually created a text file as follows tablename%number of splits
ex cdcls%5
cdhdr%4
I saved the file in my system and when the installer asked I gave the txt file and run the table split. But in this split I took only top 5 tables to check. I got the whr.txt file and I used that file when I am exporting the database instance. Figure as follows.
fig1: The txt file i created manually with the top 5 table names
Fig: 2 I gave the whr.txt file while I am exporting the database instance export.
I did not run any migration monitor or distribution monitor here. When it asked me I just went with the default options.
The downtime I met here was same to my direct export downtime. 