United Precision Products, a Michigan machine tool plant, makes aircraft engine parts so exact that they come within one or two ten-thousandths of an inch of their designs.

But executives at the company have learned that getting America back to work in the middle of a pandemic is nowhere near as precise or finely calibrated.

The Dearborn Heights factory, which has both military and commercial customers, was deemed an essential business and so it stayed open in March when the rest of the state shut down.

Then an employee contracted the coronavirus and ended up in a hospital’s intensive care unit. When a second worker came down with virus symptoms, the 73-year-old company temporarily shut its doors for the week of April 13 and hired a firm whose technicians came in hazmat suits and sanitized the entire place. Even papers on the desk of the vice president, Robert Bloom, were sprayed and left with the edges curling upward.

United Precision Products today is a case study in the difficulties, and possibilities, of reopening the American economy.

Once the plant had closed because of an infection, the owners had to do something extra to restore confidence, bring people back to work, avoid legal problems — and head off a possible outbreak. Testing became a key part of the plan.

On April 15, United Precision Products brought its 41 employees to the company parking lot at staggered intervals. They stayed in their cars while spitting into vials with bar codes that keep the results confidential. Those vials were sent to DxTerity, a private Los Angeles testing firm, and a day or two later, the results were in: Two employees tested strongly positive for the coronavirus — one who had been sick earlier and one who was asymptomatic and knew nothing of the infection. Four others got more mildly positive results. Those six were sent home to call their doctors.

The plant reopened on April 20, albeit with a reduced staff. In addition to seven infected workers who were quarantined, one other worker, uneasy about his co-workers testing positive in mid-April, held out for roughly a week before returning to the plant.

The machine tool plant has tested its employees weekly for the past five weeks, using kits provided free as part of an experiment by DxTerity, which plans to sell directly to corporations anxious to figure out a way to bring employees back while avoiding new outbreaks.

Testing can help businesses do that, DxTerity says. It takes 24 hours to get the results, so workers could spend a day on the job before the results come back.

“You don’t know what people do outside the plant,” said Gary Winkler, the company’s chief executive. “They go home or go to the bar and violate the social distancing rule and come back and you don’t see it.”

Until it’s too late.

One of the workers who tested positive April 15 had symptoms before and had been hospitalized. But he had finished two weeks of quarantine, and his physician said he could return to his job. Testing positive again was a setback; it meant he still had the virus and could spread it to other people.

“He would have been back in the workplace even though he was still a carrier,” Bloom said. “That [test] definitely worked out in our favor.”

Six days later, the worker tested positive yet again. “To me that shows there’s a problem still out there,” Bloom said in an interview last month.

The second worker who tested strongly positive April 15, even though he showed no symptoms, became ill and is still out sick.

“We need testing to get back to work safely and to stay open,” Bob Terbrueggen, chief executive of DxTerity, said in an email. “Overall symptoms alone aren’t sufficient to determine who is infected and who might be contagious.”

Terbrueggen has been running pilot programs with United Precision Products and other companies, mostly pharmaceutical and bio-tech firms. He plans to sell his testing kits to companies that screen their own employees. It’s not that different from Walmart checking employees’ temperatures before they can start work, he says. Others have compared it to a firm carrying out urine tests to check for illegal drugs.

Some health experts are cautious about the widespread use of tests to screen workers, especially given the scarcity of testing devices in many parts of the country.

Albert Ko, a professor at the Yale School of Public Health, said the priority for testing should be places where there have been outbreaks: nursing homes, prisons and densely packed poor communities of color.

“If we’re thinking about reopening, whether it is Connecticut or any other section of the economy, we’re going to have to protect those vulnerable populations,” he said.

Rajaie Batniji, a physician and co-founder of a firm called Collective Health, which helps self-insured businesses manage their health benefits, says that regardless of the need to test high-risk populations, the burden of reopening the economy will fall on businesses. And even employers who implement some protections can still face risks.

“We haven’t seen clear guidance from national institutions as to what constitutes reasonable risk reduction in the workplace,” Batniji said. “And it’s pretty clear that not every employer can play armchair epidemiologist.”

As the economy reopens, the number of coronavirus cases is likely to expand, and temperature checks and symptom questionnaires are not enough to reduce the risk of a workplace outbreak, said Scott Gottlieb, former Food and Drug Administration commissioner.

“The way to get people back to work is to have broad testing infrastructure in a robust way,” Gottlieb said in an interview.

“There are jobs where you come into contact with a lot of people — transportation safety, flight attendants, assembly lines, teachers,” he said. “It’s important to push testing into those work sites.”

Reopening the nation’s economy means doing on a massive scale what United Precision Products is doing in its parking lot.

“To allow people to return to work and reopen the economy before there is an effective vaccine, our public health, government, and business leaders need information about who has COVID-19, who needs to be isolated or quarantined, and who may be immune due to previous infection,” Sen. Patty Murray (Wash.), ranking Democrat on the Senate Health, Education, Labor and Pensions Committee, said recently in a statement. “The only way to get that information is testing: ubiquitous, fast, free testing, which must be followed by precise contact tracing efforts and the integration of data from national surveillance systems.”

The Harvard Global Health Institute said the country needs to test 900,000 people a day to have a better understanding of the extent of disease spread and where resources should be concentrated.

At United Precision Products, however, wedged between an Auto Zone franchise and a used car establishment, the focus is on its own workplace.

It has made some changes to make workers feel less afraid. Even before the pandemic, the factory placed machinery so operators were more than six feet apart. The loading dock switched to one person instead of two. Visitors now need to be buzzed in. There are different shifts for eating in the cafeteria to create more room between people.

“The good thing about this type of testing is you’re going to have the ability to set up on a weekly or biweekly basis and continue to test your work staff so that you’re sure they’re not bringing it into the workplace,” Bloom said.

If it’s costly, it’s still worthwhile for many businesses. DxTerity’s Terbrueggen says one of his customers is a pharmaceutical plant, which is testing its workers twice a week. “If 30 people at a pharma company are making product worth millions upon millions of dollars, you don’t want to shut it down,” Terbrueggen said. DxTerity’s test costs between $75 and $125 each, depending on the size of the order.

Bloom said frequent testing also helps deal with “the fear factor that everybody has, even those who don’t have the virus.”

“They get just the little symptom and they really wonder whether they’re coming down with it,” he said.

Winkler and Bloom are interested in the Swedish model, where the government has taken a relatively hands-off approach to the pandemic and is assuming that enough of the population will be lightly infected and acquire “herd immunity” that would blunt the virus’s impact. So far, however, Sweden’s death rate continues to run much higher than that of its Nordic neighbors.

“The herd immunity is something that really makes sense,” Winkler said. “Where they protect the vulnerable and let the virus sweep through the healthy people.”

But most companies are worried about things closer to home.

“As soon as we start telling people to come in, we are telling people to come back to work in a space where the virus is likely present, is likely transmittable, and because we don’t yet have access to widespread testing we are also asking them to engage in uncertainty, ” Joshua M. Davis, a lawyer at the firm of Goulston & Storrs, said in a recent webinar titled “Back to Business: Returning to Work in the Covid-19 Era.”

“As an employer you face a risk,” Davis added. “You can assume gross negligence about protecting people from covid-19 could lead to liability. One reason you want to think about these things is that you could actually have a lawsuit about an employee who gets sick.”