when a PhD position is re-posted after I had an interview I had a PhD interview and they said this decision will be made by the end of this week.
I haven't received any email from them yet.

However, I saw a new advertisement about the same position as I applied a few days ago.

Does this mean I am rejected?
Should I send an email to an administers to ask if I had failed?
It could have a lot of reason why a position is reposted. Computer mistake, additional position, confusion with another position, people not talking properly to each other, fraud, rejection, ...
Don't do anything at least until the end of this week (which is near)! Do not look at their homepages if this makes you nervous.

In the meantime, live your life as if you did not get this position. Apply for other jobs etc.
If you really want to get a definite answer from them and they do not call you, I would give it two more weeks (could vary by locale) until you call them. Do ask for feedback and do not call your rejection a "failure". In most interviews, people do not fail (except there is a special test) but it comes out that they don't fit the position well enough because of other interests.