Redundancy is your friend.

Especially if what you are monitoring is mission critical, you want to be able to monitor your site, but you also want to something to monitor your monitoring software. What happens if it turns out the machine watching your server also went out in the same power failure?

I would say you want something like this:

• Server A is serving your pages.
• Server B is separated far enough from Server A so that its unlikely that they would be affected by the same outages (or at least you would have another way of knowing if they were).
• Server B monitors server A.
• Server A monitors server B.

There are other points to consider. For example, how does your software run? Is it a daemon? Do you have something that will catch when the daemon dies? Is it running by cron? What will let you know if cron dies?

The other item is monitoring vs. management. Its far better to have a report that says "Hey your server went down and I restarted it for you, everything is ok now." then to have a report that says "Hey your server is down, your paying customer will be complaining soon, hurry up and restart it.".