DETROIT—U.S. auto safety regulators have stepped up a series of investigations into engine fires that have plagued Hyundai and Kia vehicles for more than six years. The National Highway Traffic Safety Administration says a new engineering analysis investigation covers more than 3 million vehicles from the 2011 through 2016 model years. The agency has received 161 complaints of engine fires, some of which occurred in vehicles that had already been recalled. Engine failures and fires have dogged the Korean automakers’ vehicles since September 2015 when the company issued an engine failure recall. Since then it has issued at least eight more recalls for a host of engine problems, according to NHTSA documents posted on its website Monday. The agency says it’s opening the engineering analysis to evaluate whether previous recalls covered enough vehicles. It also will monitor the effectiveness of previous recalls “as well as the long-term viability of related …