Shutdown.exe is used by Windows for restart and shutdown procedures, usually related to having a need to reboot due to windows updates or shut down due to problems, or for network administrators to shut down the system remotely. There are probably some other applications to this command as well.
A malicious infection could possibly take control of it. I'd run full virus AND malware scans, preferably with separate utilities like whatever antivirus you use and a malware scanner like Malwarebytes. Running a second opinion scanner and a Rootkit scanner as well might be a good idea if nothing turns up on the standard scans. There is info here:
http://www.tomshardware.com/faq/id-2602295/protect-remove-virus-malware-infections-layman.html
The other possibility is that somebody has remotely accessed the system and implemented a script to initiate the shutdown. Make sure windows firewall is enabled and that your router firewall protections are not compromised. Check your router logs to see if there is an intruder on the network. If you have wireless access enabled on your router, changing the password might be a good idea. Make sure your operating system has remote access disabled. You can do that by going to control panel, system, advanced system settings, remote tab, uncheck "allow remote assistance connections to this computer".