AIX

aim performing this steps to investigate why server was shutdown, but i don't find any reason , as no user was connected to the server ???
who can i find hte reason why system had shutdown?

Nearly you have covered everything except checking your HMC's logs
I think you have quoted from this article all you need is to it reread it thoroughly you might put your hands on something significant.
Otherwise call IBM if you still have a valid support contract have a look here

i did not find nothing, could it be a sofware crash and or excissive use of cpu?

Some application crashes might system bring system down with unexpected shutdown due, But I'm not sure if excessive load on processor might crash the OS to shutdown unexpectedly especially in AIX never been in such situations. If you are concerned and the system is critical to you and this is not the first occurrence of unexpected shutdown try to call IBM and investigate with them .

If this is this a clustered system like rac - oracle keeps rebooting boxes when it looses heartbeat and the only trace for the root cause is usually the logs of oracle - other clusters do similar things

Another very common reason is that your system is pinning more memory than it should - once you reach the systems threshold (usually something around 84%) AIX will reboot the node. This most commonly happens on sybase boxes - or if you are running out of paging space but that leaves traces in errpt

regards
zxmaus