As the others have said this could be a quality issue, however I have had similar issues with the iPhone 6+ which was easily rectified.
The iPhone 6+ has two rather long connectors from the LCD and Digitizer Assembly, one for each respectively. Due to their length, these connectors sometimes have issues making full contact with the headers. As they are slightly malleable, you will find they often flex in a concave fashion, or perhaps one end will be lifted. Removing and straightening the connectors so that they make full contact with the header is a quick fix, and can sometimes get you out of trouble if a new screen isn't displaying or the digitizer isn't functioning correctly.
Again, this may not be the issue, but as the iPhone 6+ has longer connectors for the screen assembly, it is worth checking out.
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