The production, written by Miller's father, will run Sept. 6-22.
"The playwright's first commercial success is the post-World War II story of a seemingly all-American family, the Kellers, caught up in the struggle between personal responsibility and their duty to the nation," press notes state.
Robert A. Miller is serving as the school's Conservatory of Performing Arts Distinguished Master Artist-in-Residence for the 2013-14 season.
The REP's 2013-14 season also includes Soldier's Heart, by Tammy Ryan, Heads, by EM Lewis, and By the Way, Meet Vera Stark, by Lynn Nottage.
Tickets and more information can be found by calling (412) 392-8000 or visiting pittsburghplayhouse.com.