Sergeant Muller was a member of Company G, 2nd Battalion, 7th Infantry Regiment, 3rd Infantry Division. He was listed as Missing in Action while fighting the enemy in North Korea on 15 December 1950. He was presumed dead on 31 December 1953. His remains were not recovered. His name is inscribed on the Courts of the Missing at the Honolulu Memorial.

Muller was awarded the Purple Heart, the Combat Infantryman's Badge, the Korean Service Medal, the United Nations Service Medal, the National Defense Service Medal, the Korean Presidential Unit Citation and the Republic of Korea War Service Medal.