Try this:
if ! pgrep process_name; then
/home/data/process_name &
echo "$(date): Process start" >> /home/data/log.txt
fi
If do you want to kill process and then start it, try this:
if ! pgrep process_name; then
/home/data/process_name &
echo "$(date): Process start" >> /home/data/log.txt
else
killall process_name
/home/data/process_name &
echo "$(date): Process start" >> /home/data/log.txt
fi