How can I tell if my name server is down?

Sometimes our server down, so we cant really access to the site. example, example.com the server IP is 123.123.123.123. It point to the ns1.nameserver.com and ns2.nameserver.com.

So let say one day, i can access to 123.123.123.123, but not example.com.

is that mean the ns1.nameserver.com/ns2 down?