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Checking uptime/downtime on a regular basis is good. Checking if pages and content display correctly would be even better:
It happens from time to time that cache conflict or other issue cause pages to display wrongly (e.g “raw” content, with no css or images loaded).
Adding to the uptime check something similar to the “Safe Update Check” (in plugin update automation) would allow to alert if selected pages content changes more than X%.
Administrator could be alerted first hand and do what needs to be done (e.g cache flush, php restart, …).