The number of airline complaints to the government was the lowest in 15 months in May, and air carriers also recorded their best on-time performances, according to the Transportation Department.

The department said Monday that its consumer affairs office received 36 percent fewer complaints from airline passengers than during the same month in 1987. For the first time since February 1987, the number of complaints dipped below the 2,000 level at 1,820.In April, the latest month for which there was on-time information available, the 14 largest airlines had 82.6 percent of their flights arriving within 15 minutes of schedule, compared with 78.8 percent in March, the department said.

The April figures were the best since the department began monitoring on-time performance last September and in part reflected good weather during the month, officials said.

America West had the best performance during April with a 90.8 percent on-time arrival rate, followed by Southwest Airlines at 90.3 percent. Pacific Southwest Airlines reported a 91.1 percent on-time rate, but that covered only the first eight days of the month before its operations were incorporated into USAir as a result of last year's merger.

Eastern Airlines, which has been plagued by labor tensions, had the worst on-time arrival rate among the 14 airlines, with 75.5 percent of its flights arriving within 15 minutes of schedule. Pan American World Airways reported a 76.5 percent on-time mark.

The airlines also misplaced fewer bags during April with 6.53 baggage complaints for every 1,000 passengers flown, compared with 7.48 reports the previous month and 11.83 reports in January.