The nation's airlines did a pretty good job of delivering their passengers on time this past summer, with more than four of every five flights arriving near schedule, government figures show.

The Transportation Department said Wednesday that in August the 13 leading airlines had an on-time record of 83 percent, the second best since monthly reports have been available. The only better month was June, which had an 84.3 percent on-time record, the government said.The Salt Lake airport had the best arrival record in August, with 91.4 percent of the flights landing within 15 minutes of schedule. The Pittsburgh airport, where runway repairs have contributed to delays, had the worst record, with 71.3 percent of the flights landing on time.

From April through August the airlines reported better than 80 percent of their flights arriving within 15 minutes of schedule - considered on time by the government - each month.

The summer months normally have delay problems because of the heavy vacation travel as well as frequent thundershowers and other weather problems, according to industry experts.

Two years ago the summer travel months brought rec-ord flight delays and loud complaints. The Federal Aviation Administration reported more than 1,000 delays a day because of air traffic control problems alone in the summer of 1986. That was an increase of 25 percent over the previous years. No statistics on total number of delays were available at that time.

The delay problem eased a bit in the summer of 1987, but congressional pressure and loud protests from air travelers prompted the department to order the airlines to provide monthly on-time performance reports beginning in September 1987.

During the first year of the reporting requirement, the air carriers averaged a 78 percent on-time record, the department said Wednesday.

Air traveler complaints to the department's consumer affairs office have declined sharply, according to the figures provided Wednesday.

The on-time statistics cover the 13 leading airlines and do not include delays attributed to mechanical problems, although they do include delays caused by poor weather.