I have had similar issues with an almost new Asus E402SA laptop running Windows 10. Kept shutting down randomly, on the odd occasion the sreen would become corrupted, or it would freeze, and yet sometimes it was fine for hours. I tried several things, changed BIOS graphic settings, turned off all background tasks, reduced start-up tasks to a minimum etc, but still the shutdown problem persisted. Windows 10 Update had updated a load of device drivers for me but that didn't change anything. I then checked all the main component drivers in device manager manually and all drivers seemed ok. But still the proble occurred, very frustrating. Then I discovered somewhere else on this board that System Device drivers may not get updated by Windows Update and I had not checked those at first as there were many of them and I thought they would be basic drivers which would be fine. However, I checked all these manually and found that the ASUS Wireless Radio Control Driver had an updated driver - v1.0.0.8 dated 24/10/2017. I updated this driver and re-booted, and hey presto! No problems so far! However, I will monitor over the next few days and will confirm if this has fixed the problem. But worth checking this driver in your Asus laptop. Fingers crossed, as this has been a right pain for months!