Iphone 5 silent texts and incoming calls

My partner has an IPhone 5 - all up to date operating system

I called him yesterday and it rang once, and then came back with User Busy. This also happened with another friend calling him.

He said he is not getting all calls, and some of the text messages are not coming through

I checked last night, and he had the Half Moon in the top right hand corner. I found out this was No Notifications. Doh

This has now been sorted, but it appears he can receive some texts and calls, but not all. I know he is not a techie person, so he might have changed something without realising. The volume is up, and notifications is on

Does anyone have any other ideas please?