One problem related to other fuel system pump has been reported for the 2016 BMW 328. The most recently reported issues are listed below.
I was driving appx 45 mph (speed limit) on a suburban street when the car ran out of power, slowed down to a crawl and became totally limp. Meanwhile, the image on the navi screen stated, "powertrain failure, drive moderate speed" or something like it. I managed to make a very slow left turn onto a cross street b/c I was in shock. I was almost killed by an oncoming car going 45-50 mph. I had the car towed to rusnak BMW; after investigation, they stated it had a "bad fuel pump," and that they have "countless fuel pump problems with BMW diesel cars". The car now has a new fuel pump. I could have died!.