The recent crane accidents included one on Nov. 29, when the 110-foot arm of a crane made a “loud pop” and then “fell uncontrollably” to the side of the rig, according to an internal agency incident report. The crane had just been used to lift four workers between a supply ship and a drilling rig working 50 miles offshore. Before the arm came to a rest, it punched a hole in a fuel tank and caused a diesel fuel spill that left a 50-yard-wide sheen for five miles, the report said.

In another incident in mid-December, a bundle of tubing weighing hundreds of pounds fell as it was being lifted by a crane. A large pipe slipped out and dropped 120 feet, missing workers who were on a ship below, the agency said.

One worker did die in December on a drilling ship in an accident when a pipe-moving device — not a crane — crushed him when he entered an area where he was not supposed to be standing.

“No one wants to face the family of a worker who dies or is severely injured because we didn’t do our jobs correctly, or because we failed to recognize that the risks present on site were beyond acceptable bounds,” Brian Salerno, then the head of the offshore safety agency, said in remarks to industry officials in July 2015 after the new crane safety rules were proposed.

“So let’s see what we can do to reverse those trends,” he said.

But the problem has only worsened since then, according to Interior Department records released to The Times. The rate of lift-related offshore accidents last year increased by more than 4 percent, reaching the second-highest annual level in the past decade. On average, there was one incident for every 13.5 offshore platforms or drilling rigs, according to agency data.

Arena Offshore was among the companies that had multiple lift-related accidents. In one, a worker was severely injured when he was pinned against a handrail as crews were using a crane to lift a 10,000-pound construction tool house. The operator of the crane could not see the area where the offshore worker was standing, investigators found.

In another case, involving Energy XXI, a motor failed, making it impossible to control the crane. A basket carrying four workers swung out of control, injuring three of them, an incident report says.