If you need to know the time that a linux or unix process has been alive you can check when that process started, to do so write on the command line the following command.
ps -p process_id -o lstart
The proccess_id is the id you find when you see the information of the process using the ps command.
ps -ef |grep weblogic
Will return the weblogic processes runing, the first number of each line is the process id.