In an age of sophisticated computer modeling, Boeing engineers relied on the same test used for tiny cellphone batteries to gather data about the safety of the heftier lithium-ion battery on its new 787 jets: They drove a nail into it to see what happened.

As the nail pierced one of the eight cells, it accomplished its goal of setting off a short circuit. Only smoke, not fire, belched from the battery.

But the test and other evaluations that Boeing conducted while the plane was in development proved to be far off the mark in predicting what would happen when the plane was in use and led Boeing to severely underestimate the likelihood of a fire in the 63-pound battery.

Now, as Boeing tries to recover from a battery fire on one of the jets and a smoke incident on another that led to a worldwide grounding of the 787s in January, federal officials say it is crucial that the company collect better data this time from its laboratory and flight tests. That is particularly important, they said, because the cause of the jet’s battery problems is still unknown.

Boeing won approval Tuesday from the Federal Aviation Administration to begin an extensive array of 20 types of tests to determine whether its proposed new battery protection system works.

“It is clear from what happened in January that there are other ways for the batteries to catch fire that clearly weren’t captured by the nail test,” said Donald R. Sadoway, a materials chemistry professor at MIT.

He said the test — which is standard in testing lithium-ion batteries in cellphones, laptops and electric cars — measures just one kind of failure mode and represents an extreme short circuit of the battery in a very short period.

“It can work on a cellphone battery with a single cell, but you’re talking about a very different configuration here,” he added.

A preliminary report on the fire that occurred in a plane parked at Logan Airport in Boston airport on Jan. 7, released last week by the National Transportation Safety Board, provided new details of Boeing’s initial battery testing, including its reliance on the nail test for some of the basic data on the odds of incidents with smoke and fire.

The board’s report said that Boeing had also gathered information from companies using the lithium-ion batteries in other industries and, based on that and the test data, calculated that the odds of smoke being emitted from a battery was only 1 in 10 million flight hours.

Given that Boeing has never made its own batteries, it assigned other crucial tests to its subcontractors, including GS Yuasa, a Japanese battery maker, and Thales, a French company that oversees the battery charging system.

The FAA also delegated much of the testing to Boeing, except for a safety assessment conducted once the plane’s electrical power system was certified. The FAA’s decision to delegate some of its certification authority was done under a decades-old program meant to help the agency keep up with fast-changing technology but also to fill a gap in its own expertise.

In the course of the original testing, the batteries were also subjected to other kinds of destructive tests, including provoking an external short circuit, overcharging the batteries for 25 hours, subjecting them to high temperatures of 185 degrees Fahrenheit for an extended period, and discharging them completely. Boeing found that none of these tests resulted in a battery fire, according to the safety board’s report, leading it to conclude that the chance of a battery fire was 1 in 1 billion flight hours, a negligible probability. The Boston fire occurred after the entire 787 fleet had flown with passengers for only 52,000 hours.

FAA and Boeing officials said they did the best they could, given what was known about the batteries when the agency approved them for the 787 in October 2007. The innovative plane, which uses lighter-weight composite materials to cut fuel costs by 20 percent, makes more extensive use of the new batteries than any other commercial aircraft, and the FAA imposed a series of special safety conditions to compensate for that risk.

But in March 2008, the RTCA, an advisory group that suggests regulatory measures, released new and more rigorous guidelines for testing lithium-ion batteries — standards that Boeing says it will meet in its new round of testing.

The safety board’s report said that Boeing continued to test its original battery design in 2010. But the company, which was busy dealing with many other problems that had led to multiyear delays in the 787 program, did not change its test plans to follow the RTCA guidelines. It was not obliged to do so under the law, and Boeing officials said they had not run into any problems with the battery in tests anyway.

It is not clear whether the nail test will be included in Boeing’s new testing regimen. In the test, a metallic nail is driven with blunt force by a machine into a battery to provoke a short circuit. The test is supposed to show whether the battery cells are properly insulated from one another. If they are not, this increases the risk of a thermal runaway where one cell overheats, catches fire and the fire cascades to the other battery cells.

But according to a 2011 presentation by the National Renewable Energy Laboratory, a federal research lab, the nail test and other so-called abusive test methods are not representative of the kinds of failures that can happen when the batteries are used in real life. Further, the report found that many of the failures that occurred with lithium-ion batteries in laptops or cellphones originated in an internal short “that was not detectable or predictable” during manufacturing.

Boeing officials said they now had a deeper understanding of what might cause the batteries to fail and how to minimize that possibility. After weeks of engineering work, Boeing has proposed redesigning the batteries to insulate the eight cells from one another to keep a short circuit in one from cascading to the others, as investigators believe happened on the plane parked in Boston.

Boeing plans to enclose the batteries in stainless steel boxes, which are more resistant to higher temperatures than the earlier aluminum ones. While the original batteries could leak hazardous substances into surrounding bays, Boeing also plans to create tubes made of titanium to vent any overheated air or hazardous gases outside the planes.

Boeing is hoping it can rapidly complete the tests of the new design and get the planes refitted by mid- to late April, although government officials expect a slower timeline. While domestic regulators have approved testing of the redesigned system, Boeing must still convince Japanese regulators and is sending a delegation to Japan to present its technical fix this week.

Ray Conner, the chief executive of Boeing’s commercial plane division, said in a statement Tuesday that this “permanent resolution” was designed to “significantly minimize the potential for battery failure while ensuring that no battery event affects the continued safe operation of the airplane.”

But safety and battery experts are still questioning whether regulators can approve a permanent fix even when the cause of the fire remains unknown. Boeing has brought in a number of outside battery experts, including some from General Electric and companies like General Motors that make electrical cars, to help it design the new system.

One of the plane’s two batteries provides power to start up the cockpit instruments. The other battery helps provide power when the plane is on the ground.

Boeing officials said the batteries had never had any serious problem during more than 1 million hours of laboratory and flight testing before the first 787 was delivered in late 2011.

Hans Weber, an aviation consultant, said Boeing’s new effort to eliminate every possible source of a problem “is what I would call brute forcing it, which is what you do when you don’t know what went wrong.”

Still, he said, “One of the challenges of new technology is that it takes time to learn the ways a technology can fail. And the only way to learn more is to start using the planes again.”