It is not clear to me exactly what you would like to monitor, but at a very high level you can tell how long your system has been up with applications like Android system info, which will tell you system up time, which you can use to determine when the system last rebooted.
I don't know for sure, but possibly a security program will list reboots in its logs along with any issues it has detected. Other programs that record their activity are also a possible source.
I am not sure if it has a startup event, but Tasker may give you some possibilities as well.
Sent from my Nexus 7 using Tapatalk 4