[2] After continuing at Purdue in a temporary position, Trappey became an assistant professor at Iowa State University in 1990.
She returned to Taiwan in 1992 as an associate professor of industrial engineering at National Tsing Hua University (NTHU) in 1992.
She was promoted to full professor in 1996, and became founding director of the Electronic Business Center in 2003.
While continuing to hold her affiliation with NTHU, she also became dean of the College of Management and chair professor at National Taipei University of Technology from 2008 to 2011.
Since 2017 she has directed the Advanced Manufacturing and Service Management Research Center at NTHU.