Brinzo is currently chairman and chief of iron ore pellet and magnetite supplier Cleveland-Cliffs and Roberts is president and chief of Foundation Coal Corp.
Phelps Dodge chief J. Steven Whisler was elected chairman of the Audit and Finance Committee.
Board members serve a two-year term.
“We’re a stronger and better association because of their voluntary efforts and the participation of our entire Board and membership,” NMA president Jack Gerard said.