There is something called as SNMP , which is used to configure notifications in the weblogic server .
The notifications can be configured for events such as change of server health status too.
The above guide gives you idea on this.
Follow this note. Using this, you can get notification to your email id about the weblogic status.
How to Send Notification E-mails Based on Defined Criterias in Weblogic Server (WLS) [Video][Article ID 1314023.1]
How to Configure WebLogic Server to Send a Notification When Its Configuration is Changed[Article ID 1377733.1]