Spirit Airlines triggered the most complaints

Talk about a patch of rough air.

According to a new report from the Department of Transportation, Spirit Airlines last year had the worst on-time arrival record of 13 U.S. carriers. What's more, the low-cost airline also had the highest rate of consumer complaints over that time span.

The transportation department's data, released Thursday, showed that 11.73 out of every 100,000 customers who flew Spirit last year complained about some aspect of their experience. That rate was dramatically higher than the industry's overall complaint rate of 1.9 per 100,000 fliers, the DOT said.

Spirit's performance may also explain why the overall complaint rate for airlines was up 47 percent last year, although the industry had more on-time arrivals, did a better job handling bags, and bumped fewer passengers from oversold flights.

The DOT did not include Spirit in its industry complaint calculations before 2015. Spirit has not yet responded to CNBC's requests for comment.

Of the 2,069 complaints filed by Spirit passengers, the DOT said the largest percentage were related to flight problems. They were followed by reservation, ticketing, and boarding issues, and then baggage complaints.

Last spring, Spirit added non-stop service to 10 new destinations. That expansion and the pressure it put on the airline's margins were part of a rocky 2015 for the carrier, with Ben Baldanza, who led Spirit's rapid growth for years, being replaced as CEO last month.

Despite Spirit's woes, the DOT said the industry's overall on-time arrival rate of 79.9 percent was the best since 2012.

To see the full list of the most on-time U.S. airlines, see below.

Correction: This story has been corrected to reflect the proper rate of complaints for the overall industry and Spirit Airlines.