The experts provided real-life examples. To avoid appearing illegally overcrowded, one factory moved many machines into trucks parked outside during an inspection, a monitor said. Whenever inspectors showed up at certain plants in China, the loudspeakers began playing a certain song to signal that underage workers should run out the back door, according to several monitors. During inspections in India, some factories displayed elaborate charts detailing health and safety procedures that, like stage props, were transferred from one factory to another, another monitor said.

For monitoring companies with major retailing clients, the auditing regimen can be nonstop. The territory itself is daunting — 5,000 factories produce garments in Bangladesh alone. A retailer that uses 1,000 factories worldwide might want to pay no more than $1,000 an inspection — that could mean a one-day, check-the-box audit — instead of $5,000 for thorough, five-day inspections. That would cost $1 million instead of $5 million.

“You have this intense price pressure downward on these inspection firms, turning them into a commodity business,” said Mr. O’Rourke of the University of California, Berkeley.

Auret van Heerden, president and chief executive of the Fair Labor Association, a nonprofit group that Apple uses to monitor its Foxconn factories in China, said many inspectors were too rushed. “Many are doing a factory a day, and many auditors, more than one factory a day,” he said. “They’re on a plane and going to a new city the next day. They don’t have much time to think about it or dwell on it.”

Despite some improvements, many supply chain experts say monitoring has inherent shortcomings. Not long ago, Nike and other sporting goods companies were shaken by revelations that children, ages 5 to 14, toiled up to 11 hours a day making soccer balls for them in Sialkot, Pakistan.

A study found that half of Pakistan’s soccer ball workers were making less than the minimum wage, with many stitching the balls’ panels together at home, making it hard for factory monitors to unearth such violations.

Nike responded by requiring its main contractor there, Silver Star, to consolidate production in one big factory. Knowing how skilled many contractors have become at gaming the monitoring system, Nike took an unusual step and ordered Silver Star to set up a system of elected worker representatives who would be charged with speaking up about safety problems, wage violations or other issues.