The former SecDef had ordered the F-16, F-22, F-35 and F-18 fleets brought to 80 percent mission capable rates.
The book is styled as a three-part course in leadership tracing Mattis' 40-year career.
The former defense secretary said more leadership guidance is necessary for the change to be implemented.
"We're going to have to learn from our past," he said, pointing to the rise of ISIS when U.S. troops pulled out of Iraq.
The former defense secretary bares all in an editorial Wednesday in The Wall Street Journal.
Dunford's comments follow a widely read new editorial from former SecDef Jim Mattis warning of the dangers of tribalism.
Retired Marine Gen. Jim Mattis, the former defense secretary, will serve on the board of directors of General Dynamics.
The mother of former Defense Secretary Jim Mattis died Sunday. Lucille Mattis, of Richland, was 97.
When he resigned as defense secretary last December, Jim Mattis thought it might take two months to install a successor.
"Call Sign Chaos" should be far different in tone from such scathing best-sellers as James Comey's "A Higher Loyalty."