All good points above, but only works if the Delphix Management component is working. What if it's down? It cannot send alerts.
In addition to configuring alerts and notifications, you should use a simple HTTP/HTTPS probe from your monitoring solution of choice. They all have such a probe, and your company is almost certainly already using one to monitor other important web based software, you just need to find the right people.
The probe typically just hits a web page every minute and looks for a 200 response from a web server, and as long as they get one everything is judged to be OK. It's very simple, and about 99% effective.
The reason only 99% effective is false positives and negatives. False Positive: the Management component might just be slow, not down. (Personally...I'd like to get alerted for that). False Negative: hypothetically the Management component might be up but the engine is still "unhealthy". (But you should get an Alert for that!)
Just remember, you need BOTH the HTTP/HTTPS probe AND the Delphix alert system to successfully monitor your engine health.