After a couple of recent upgrades from ArcGIS Server 10.2.1 to 10.3 and then from 10.3 to 10.3.1 we had some issues with some of the Server System Tools within the ArcGIS Server Manager. In one case a couple were missing, in another case some tools did not function as expected.
The suggestion would be to have some kind of ArcGIS Server Upgrade Integrity Tool that would check and verify the installation went correctly. It would also verify that the ArcGIS server site (either new or existing) is operating correctly with all needed tools. This function could be bundled as part of the upgrade process and would automatically execute and provide feedback if all is OK or if the server site (where the tools are located) is corrupt, etc.
Thanks.