This was the first time large lithium-ion batteries were used aboard a commercial jet. The 787 has two of them, one for its auxiliary power unit, or A.P.U., and a second to turn on its flight deck computers.

Boeing had initially determined that a battery cell might fail in one out of 10 million flight hours. Instead, by the time the two episodes happened, the 787 fleet in service had logged fewer than 52,000 hours, according to the safety board.

“The incident resulted from Boeing’s failure to incorporate design requirements to mitigate the most severe effects of an internal short circuit within an A.P.U. battery cell,” the report said. It also faulted the F.A.A. for failing to identify the design problem.

“Boeing should have taken a more conservative approach in its safety analyses,” it said.

The N.T.S.B. had already concluded that the battery failure came from an internal short circuit in cell 5 or cell 6 and led to a fire that propagated to other cells — known as a thermal runaway. But the battery was too damaged for specialists to figure out what had caused the internal short in the first place.

But its investigation found that the manufacturing process allowed defects that could lead to internal short circuiting. GS Yuasa, it said, “did not test the battery under the most severe conditions possible in service, and the test battery was different than the final battery design certified for installation on the airplane.”

Shortly after the report was made public, GS Yuasa issued a statement through a United States-based public relations firm and defended its manufacturing methods.

“We appreciate and respect the N.T.S.B.’s final report, although the root cause of this internal short circuit remains elusive,” GS Yuasa said in a statement. “We remain fully confident, however, in the quality and safety of our batteries, our state of-the-art manufacturing processes and our highly skilled and trained employees.”