Some users are able to click on a details link in process list page and choose the option delete to clear the process which does not belong to them. This is only for some processes and not all. Security has been set so users can only update their own processes and view everyone's else.
This setup has been done in process profile permission list.
Any suggestions what could be wrong?
It might be something to do with permission lists? Maybe try comparing the permission lists of users with the issue and those without using the PSOPRCLS view (select * from PSOPRCLS where OPRID = '<youruser>') to identify what might be different.
See this doc
E-PRCS - How To Limit the Cancel and Delete Options on Process Monitor > Details page? [ID 662723.1]
In addition why this happens one some processes and some not could be that processes are assigned to different process groups.
And process groups are again assigned on permission lists.
So may have multiple permission lists with different proces scheduler settings for different process groups.