(Photo by Peter O'Dowd - KJZZ)

An American Airlines plane.

The Airline Quality Rating annual survey found the U.S. airline industry improved in several categories, but the rate of customer complaints increased to its highest level in 15 years.

One in three complaints to the Department of Transportation focused on flight problems - like cancellations and delays. Other complaints involved baggage, ticketing, boarding and customer service.

The Airline Quality Rating is a joint research project at Wichita State University and Embry-Riddle Aeronautical University in Prescott. By crunching data and surveying consumers, they come up with annual ratings.

Virgin America is the top-ranked U.S. airline overall, followed by JetBlue and Delta. Alaska had the lowest consumer complaint rate and Spirit had the highest.

Overall, the industry collectively improved on-time performance and the rates of bumping passengers and mishandling baggage. 

Here is the overall ranking of the nation's leading 13 airlines, according to the Airline Quality Rating. The 2014 ranking is in parentheses:

1. Virgin America (1)
2. JetBlue (4)
3. Delta (3)
4. Hawaiian (2)
5. Alaska (5)
6. Southwest (6)
7. SkyWest (10)
8. United (9)
9. ExpressJet (11)
10. American (7)
11. Frontier (8)
12. Envoy Air (12)
13. Spirit (new to rating in 2015)

The Associated Press contributed to this report.