On Monday morning, the U.S. Department of Health and Human Services kicks off a competition to redesign medical bills and the billing process for consumers. Federal health officials are overhauling health care to bring more “value” to the system. “Part of the billing challenge is trying to help patients understand what their financial responsibility is going to be as early on in the process as possible,” said Greg Meyers, an executive with the hospital system INTEGRIS Health in Oklahoma, one of the providers committed to testing the winning designs.