Dell Inspiron does not go into GRUB after shutdown from Kubuntu

I bought a new Dell Inspiron 15 3000 (Ubuntu) laptop and installed Kubuntu 15.10. No dual-boot. Kubuntu only.

Everything seems to work... with one exception: After shutting down (or restarting) from Kubuntu/KDE, the Notebook will not boot correctly a single time.

When I shut down the system everything seems ok. Then when pressing the power button I can see the Dell logo for a short time (also some kind of progress bar at the bottom) as usual. Then the screen is blinking in different shades of black, then nothing more happens. No GRUB menu. In this situation pressing ++ restarts the Notebook and GRUB is reached and everything works fine. Also succeeding restarts (without booting into Kubuntu) work without problem. However as soon as I boot into Kubuntu and shutdown/restart from there the next single boot of the Notebook will fail.

Any idea what the problem could be?