In some situations, you just need a fast way to monitor MySQL and restart your service asap in case of crash. Neither a production script nor a replacement for a real server monitoring tool (like New Relic, ...) with IP fail over, but a basic solution when you just provisioned a low budget VPS with a very limited setup and still want to get a feedback for further logs details.
1) Install mailutils
It will be necessary to send an e-mail alert.
apt-get install mailutils