This sounds remarkably like a homework assignment to me...
I'm guessing something like this covers most of your points.
property theAddress : "10.32.8.151"
set missedPings to 0 -- initialize the counter
do shell script "/sbin/ping -c 1 -t 1 " & theAddress
set missedPings to missedPings + 1
if missedPings = 6 then
tell me to quit
do shell script "/usr/sbin/traceroute " & theAddress & " &> " & quoted form of POSIX path of ((path to desktop as text) & "tracereport.txt") & " &"
do shell script "/bin/echo 'Network missed 6 pings' | /usr/bin/mail -s 'Network down' firstname.lastname@example.org"
display alert "Oops. Network failure" giving up after 5
Hey Camelot! This is great. I couldn't write this myself because I'm not very familiar with AppleScript. But I can alter your script a little to suit my needs. This is great.
I've been trying to figure out a solution to a problem like this for days! Thanks!!!
( You were awfully nice to write the script in the first place, considering how it was asked for. )