Urgent Call lets users filter out distractions by letting the most important calls or texts get through.
Users can set rules about calls that are important to them based upon the number of calls they receive within a certain amount of time, and who the call is coming from. They can similarly set up rules based on a key word or phrase in a text and who the text is coming from. Then, even if they put their phone in silent mode, they'll be alerted when those calls or texts come through.
Designs mocks are available for a pending redesign. They are located here: other/design/urgent_call_mocks.pdf.
You can download it on the Play Store or compile it for yourself.
Urgent Call is an Android Studio app.