You want to schedule integrity checks at specific times or intervals.
Use cron. For example, to perform an integrity check every day at 3:00 a.m.:
root's crontab file: 0 3 * * * /usr/sbin/tripwire --check
This is not a production-quality recipe. An intruder could compromise cron, substituting another job or simply preventing yours from running. For more reliability, run the cron job on a trusted remote machine:
Remote crontab entry on trusty: 0 3 * * * ssh -n -l root trippy /usr/sbin/tripwire --check
but if an intruder compromises sshd on trippy, you're again out of luck. Likewise, some rootkits [Recipe 9.12] can subvert the exec call to tripwire even if invoked remotely. For maximum security, run not only the cron job but also the integrity check on a trusted remote machine. [Recipe 1.8]
Red Hat Linux comes preconfigured to run tripwire every night via the cron job /etc/cron.daily/tripwire-check. However, a Tripwire database is not supplied with the operating system: you must initialize one yourself. [Recipe 1.1] If you don't, cron will send daily email to root about a failed tripwire invocation.
tripwire(8), crontab(1), crontab(5), cron(8).