From what some others and I myself have observed:
From regular containers, if you don't have a Rare (blue) rarity item at or before container #14 or earlier, then the 15th will always be a Rare (blue) item.
From Ultra containers, if you don't have an Epic (purple) rarity item at container #14 or earlier, then the 15th will always be an Epic (purple) item.
I watched Mr. Akame open some Ultra containers earlier, he also tested if the x5 openings function like this, and it seemed to match what x15s would do (if the first two x5s had no purple or above, and the third x5's first 4 weren't purple, the last container from the third x5 would be purple). He didn't try it with regular containers, but it worked at least with Ultras, so I'd also assume it's the same with regular containers as well.
 
To answer the question at hand, any given x15, whether it is Ultras or regulars, will in the very least give an item of the promised rarity once (so Rare/blue from regular and Epic/purple from Ultra containers). If it goes to the guaranteed on the very last container, it will always be whichever guaranteed rarity it is, depending on the type of container you open. From some experiences I'm fairly sure it will not be anything higher, unless you've had the guaranteed rarity earlier than the very last one, and even then it will not always go past the guaranteed rarity. I hope that answered the question.