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Disable the airplane mode
Maybe your device doesn't ring because of the Airplane mode. If you don't see the signal strength, nor the operator's name in the upper-left corner of the screen, but you see a small airplane icon, the airplane mode is enabled.
Your device might not ring because of misconfigured settings. Resetting the app preferences will restore the default settings of the apps. Follow the steps below in order to reset the apps' preferences.
Go to Settings and select Apps.
Tap the three-dot icon and select Reset app preferences.
-- Note: The screenshots are taken using a Sony Xperia M2, running on Android 5.1.1 Lollipop. The instructions mentioned here might slightly vary from one manufacturer to another.
It is possible that the ringtone you set to notify you when someone is calling you or when you receive notifications of any kind is deleted or moved to a different location. Try setting another ringtone in the device's settings.
It is very important to update the device's operating system on time as the updates contain fixes to various bugs. If you don't receive a notification about the update, check if one is available manually.