Dear Stefan,
Thanks for your reply, I have searched for not just minute but more than a hour in the blog but couldn't find the answer. and if youhave seen the code which I have pasted above, it clearly mentions that the file is opened before it is deleted. and for authorizations check also done which is successful in both the systems( Dev & QAS). The issue for me is not with the statements, but why is working fine in DEV (Sandbox) and why not in QAS? I am once agin mentioning that the authorization is successful in both the systems.
I am pasting my code onace again with the comments in RED.
SOURCE_PATH is "E:\SAPIO\IMPORT\PSP\TEST123.TXT'
OPEN DATASET SOURCE_PATH FOR OUTPUT IN TEXT MODE ENCODING DEFAULT. –giving sy-subrc value ‘0’ in TRD and ‘8’ in TRQ.
CALL FUNCTION 'AUTHORITY_CHECK_DATASET'
EXPORTING
PROGRAM = sy-repid
ACTIVITY = SABC_ACT_DELETE
FILENAME = LV_AUTHFILE
EXCEPTIONS
NO_AUTHORITY = 1
ACTIVITY_UNKNOWN = 2
* OTHERS = 3
.
IF SY-SUBRC = 1. – Authorization check is successful in both the systems.
* Implement suitable error handling here
MESSAGE E011(ZBRIM) with WA_FILES-NAME RAISING NO_AUTHORITY.
ENDIF.
DELETE DATASET SOURCE_PATH. Sy-subrc = 0 on TRD and 4 in TRQ.
Hope it clarifies. thanks and I am waiting for your reply 
Murali