The iPhone's Do Not Disturb feature ensures that your handset will not bother you when you're asleep or busy. But if you want a particular contact to still be able to reach you, you can put it on the whitelist. Here's how.
How the iOS Do Not Disturb Works
Do Not Disturb automatically mutes all calls, notifications, and alerts that you receive when your iPhone is locked. The function can be activated by tapping the "Crescent Moon" icon in the Control Center.
If you touch 3D Touch / Haptic Touch, do not disturb, you can turn it on for over an hour or until you leave the current location. You can also set Do Not Disturb on a schedule by going to Settings> Do Not Disturb> Scheduled.
"Do Not Disturb" works by default as Everything-or-change nothing. However, you can add exceptions to the Do Not Disturb filter in a variety of ways.
RELATED: How to Configure Do Not Disturb on Your iPhone and iPad
Whitelist Favorites in Do Not Disturb  The Favorites tab in the Phone app is a modern variant of Speed Dial. Add a few numbers that you often contact for a one-tap connection. The Favorites feature has some other benefits, such as the option to add the Favorites widget to your lock screen.
The favorites list is also integrated directly into the "do not disturb" function. To set up, open the App Settings, go to Do Not Disturb, select Phone, and then tap Allow Calls From.
Next, set the preference to "Favorites". This set allows anyone who calls you from your list of favorites.
iOS has the Repeat Calls option in the Do Not Disturb section. If you activate this function, a second call from the same caller will be put through within three minutes.
To add contacts to Favorites
If you have not set up the Favorites list, you can do so by tapping the Favorites tab in the Phone app. Add your family members and close friends to this list by tapping the "plus" button in the upper left corner.
Now search for a contact in your contact book.
Tap the contact to see a contact pop-up containing all contacts (including alternate numbers and FaceTime options).
Select the "Call" option and then its number.
They will be added to your favorites list. Repeat the process for all contacts for whom you want to create a "Do Not Disturb" whitelist.
Allowing contacts to use pass-by
The call-passing favorites method does not work for all users. For example, I use Favorites as a shortcut to access my frequently used contacts, which includes all my family and friends.
In an emergency only a handful of contacts should pass the filter "Do Not Disturb". If you are in the same boat, you can use the emergency bypass feature added in iOS 10.
The Emergency Bypass feature runs on a contact basis and includes controls for calls and SMS. If you have activated the emergency bypass for a contact, its calls or text can be forwarded even if you have activated the Do Not Disturb feature and the phone is in silent mode.
To enable the Emergency Call Bypass feature for a contact, open the Phone app and search for the contact.
Tap the contact to open its contact card. Then tap the "Edit" button in the upper right corner.
Swipe down until you find the "Ringtone" option and tap it. 
Tap the toggle next to "Emergency Bypass" at the top of this screen to enable the feature. Tap Done to save the setting and return to the previous screen.
You can do the same thing for text messages by tapping on "Text Tone" on the next screen and enable the "Emergency Bypass" feature.
You can repeat this process for all contacts you want to pass through the Do Not Disturb filter. Once set up, your iPhone will ring each time you're called or sent a message.