Work for Archive Log Mode ON and OFF
No shutdown is required
1. To investigate what status is the missing redo log is -
Select * from v$logfile shows which group and member is INVALID
2. From step 1, you will have the full path of the member that went corrupted. Drop this member -
Alter database drop logfile member 'fullpath/log_filename.log'
3. Add a new member to the group -
Alter database add logfile member '/fullpath/log_filename.log' reuse to group n; where log_filename.log and group n follow step 1
4. DONE

(Note: the size of the new redo log member should be the same as the other group members if you decide to use the same name and the option REUSE)