I saw a new article that said United has 5,000 flights daily. The string of mishaps while unfortunate should not be a concern. I am flying them to Europe later this year on United without any concern. My brother works for United in their SFO maintenance depot. He assures me that they follow all maintenance, documentation and safety inspections to FAA requirements. The loss of the tire at SFO is a screw up and the landing gear shop will investigate and make sure this doesn't happen again. The engine fire appears to be caused by the engine ingesting some bubble wrap, which is a FOD issue not an engine maintenance issue. I haven't seen any details on the cause of the Austin taxi event. I don't have any information on the 2 other events. United has an excellent safety record so you should not be concerned flying them.