On-time performance by the nation's major airlines improved slightly during January, but three out of every 10 flights still were at least 15 minutes late, the Transportation Department said yesterday.

Southwest Airlines, which consistently has been among the best on-time performers, had the best record in January with 85 percent of its flights arriving on time. Eastern Airlines had the worst mark with 61.5 percent of its flights arriving on time.

Overall, the 14 airlines that are monitored in the monthly report had 69.2 percent of their flights arriving within 15 minutes of schedule, compared with 66.4 percent in December.

During January, there were 148 chronically late flights, those late at least 80 percent of the time. Four of those flights -- two for Continental Airlines and one each for Delta Airlines and Northwest Airlines -- were late each time the planes flew.

Meanwhile, consumer complaints to the Transportation Department dropped sharply in February, compared with the previous month, but still were higher than the number recorded in February 1987, the department said.

The complaint statistics are released with the on-time performance statistics, although they cover different months.

There were 2,235 complaints received by the department's consumer affairs office about airline service during February, compared with 3,610 in January, a decline of 38 percent. The department received 1,574 such complaints in February 1987.

The three airlines that had the most complaints lodged against them in the two previous months -- Continental, Eastern Airlines and Northwest -- led the list again in February, according to the department.

There were 14.79 complaints per 100,000 passengers involving Continental, 11.3 complaints involving Eastern and 10.64 complaints involving Northwest, the department said.

After Southwest, the airlines with the best on-time performance in January were America West, which also was No. 2 in December, and Pacific Southwest Airlines, which soared from last among the 14 airlines in December to having the third best record in January.

America West had 83.9 percent of its flights arrive on time in January while Pacific Southwest improved its record from 57.6 percent in December to 81.6 percent in January. American Airlines, with a 75.7 percent on-time arrival rate, had the best record among the larger carriers, but Pan American World Airways dropped from having the second best record in December to seventh in January.

The airlines with the worst January record were Eastern, 61.5 percent on-time arrivals; Northwest, 61.6 percent; and Piedmont, 62.4 percent.

The best arrival rate among the 27 airports from which reporting is required came at Las Vegas' McCarran International Airport and the Phoenix Sky Harbor airport with just over 78 percent of the flights arriving on time. The worst arrival rate, 59.1 percent, was reported at Orlando International Airport in Florida.

The on-time statistics reflect all flight delays except those attributed to mechanical problems with an aircraft and include delays caused by weather problems.

During January, the number of baggage complaints received by the airlines remained virtually the same as the previous month with 11.58 complaints per 1,000 passengers flown. Piedmont Airlines had just over 18 such complaints, the most of any of the airlines, while Southwest had the least at 4.65.