As far as I can see and read Alert missions are the most effective way to get credits and can have some unique rewards that you can get no where else.
But is there any pattern to when they happen?
Sometimes it feels like I can play for hours without seeing any pop up and other times they are constantly there, sometimes even more than one is going on at the same time.
Best Answer
Every 30-40 minutes there is a new alert. It seems quite random at first, but that's because you only see alerts of missions you already have access to.
You can check the twitter account for all alerts: https://twitter.com/warframealerts
In Warframe Developer Livestream #5 they talk a bit about how alerts are generated, at 59 min. Alerts are randomly generated, except for the once started after the life stream.