standby device is rebboting,once active device went faulty F5 ltm(4000)

Do you have any error logs or the output from the LTM console?

If your system has a Service Contract, raise a service request with F5 Support.

I checked in bash mode tail -f /var/log/ltm I can able to view Present logs ,How to check 5and 6 hour back logs

You need to search in the ltm log file for the time period of interest

 grep  /var/log/ltm

if the logs have been compressed you can use zcat

 zcat /var/log/ltm.2.gz | grep 

This is weird,

satndby device is rebooting every 3 seconds

Also search your /var/log/ltm with some keywords

boot, reset, restart, action

Thanks bro

zcat /var/log/ltm.2.gz,using this command I checked ,lot of logs missed