DETROIT—Two organizations that influence many Americans’ automobile buying decisions will begin rating vehicles on how well they track behavior of motorists who use partially automated driver-assist systems. Consumer Reports and the Insurance Institute for Highway Safety say the ratings will factor into scores for new models starting this year. Automobile buyers often turn to both groups to judge the safety of vehicles. The new ratings, announced Thursday, come as the auto industry struggles with how to make sure drivers stay alert as the systems take on more driving functions. Plus, the systems are being offered in more new vehicles. Both groups say research shows drivers often rely too much on the computerized systems, even though they cannot drive vehicles themselves. At times, the systems have made mistakes and drivers have failed to take action—with deadly consequences. Some automakers have oversold the systems’ abilities in advertising, both groups said. The organizations …