First of all ensure that your replication is healthy and all copies are up to date.
The first step is to move all active mailbox databases to another DAG member so that the server can be updated.
To see a list of mailbox databases and their current active server use the Get-MailboxDatabase
In my environment has a multiple of DAG members and mailbox databases.
Move the mailbox databases using the Move-ActiveMailboxDatabase cmdlet. All of the mailbox databases are now active on server MBX2.
First check the current activation policy on the server using Get-MailboxServer.
Disabling Server Monitoring
DAG members are monitored using SCOM; this should also be disabled or placed into maintenance mode.
Conflicting Services Stopping
If the mailbox server is running any Exchange-integrated services, such as antivirus software, these should be disabled prior to the update.
Such as trend micro, Symantec Antivirus etc. and one of the important services is Data Protection Manager 2010, which may be configured to perform Copy backups from passive database copies at frequent intervals through the day. Make sure these jobs are paused to prevent errors or conflicts from occurring.
Download Update rollups from Microsoft web site which is in .MSP file form, double click.
• Then Click OK and then click on Install Updates
• Once completed click finished and restart the server.