Changing DNS contacts should never cause any kind of outage.
The Domain Name System (DNS) is a hierarchical, globally distributed system responsible for associating the name of a computer, service or other resource into an IP address for connecting to the Internet or a private network. Most prominently, it translates domain names to the numerical IP addresses needed for the purpose of computer services and devices worldwide.
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There's no such thing as a website for outage as far as I concern, You need to have skills to determine if a site went down. The issues vary, for example.
1- DDOS attack.
2- Cluster Down.
3- DNS forwarding issues.
4- TDL issues (that never happens but no bad to put it here)
5- Routing issues (load balancing, DNS round robbing, bad cache.
Again, the issue varies.
Something you can do is look for that particular website, see if you can telnet to it, try to ping it. Do a Nslookup find the name server that belongs to, see if the registrar is having issues, give them a call. Again, the problem might vary.