Check if a process is running, if not execute it again in Terminal

In OSX use launchd to to this. launchd will start a command at login or boot and if the process dies it will restart it.

The process is controlled by a .plist file formatted as defined in Apple docs the example in that manual page is for the case you ask for.

  <?xml version="1.0" encoding="UTF-8"?>
   <!DOCTYPE plist PUBLIC -//Apple Computer//DTD PLIST 1.0//EN
   http://www.apple.com/DTDs/PropertyList-1.0.dtd >
   <plist version="1.0">
   <dict>
        <key>Label</key>
        <string>com.example.exampled</string>
        <key>ProgramArguments</key>
        <array>
             <string>exampled</string>
        </array>
        <key>KeepAlive</key>
        <true/>
   </dict>
   </plist>

If you want to to start when a user logs in the this file goes in ~/Library/LaunchAgents. If when the machine boots then /Library/LaunchDaemons (which can't have access to the GUI) but this will run as root unless you add a UserName key. (Thanks to @Gordon Davisson for the correction and a reread of Apple definitions)

For ease of setting the .plist up you can use Lingon.app available from the Mac AppStore

If you wanted to do this via a shell script I'd do something like this:

#!/bin/sh
PROCESS=`ps A | grep PROCESS_NAME | grep -v grep`
if [ "$?" -ne "0" ]; then
        echo "not running"
        ### COMMAND TO EXECUTE HERE ###
        exit 1
fi

You could call that via cron every minute or so.

Why you need to actively poll for the script? Why not just put it in a shell script loop and restart it when it fails.

#!/bin/sh

let c=1
while ! php -f myscript.php; do
    echo "The script has crashed $c times so far..."
    let "c=c+1"
done

In the case it doesn't fail gracefully, polling for a running process won't save you either. It may as well keep running while not doing its job.