Alice Miller rarely has been on time for anything.

Miller can make her tee time, it is said on the LPGA Tour, only if you warm the car for her and have it waiting at the door. She then will drive to the course at 15 mph, knock a few putts around on the practice green, and shoot a yawning 68.

Her friend and fellow tour member Janet Coles recalls rooming with Miller two months ago in Malvern, Pa., for the McDonald's Championship. Miller was scheduled to tee off at 9 a.m. At 8:22, Coles said she rolled over to discover that Miller still was casually getting ready. A missed tee time is cause for automatic disqualification.

"She doesn't leave until 8:30," Coles said. "And she doesn't just jump in the car and rush off to the course. She warms it up first, right? She's about to be late and I'm laying there listening to 'vroom, vroom.'

"Then she pulls out of the parking lot at about five miles an hour. Five minutes before tee-off she's in the locker room, chatting with somebody. There isn't a panic bone in her body.

"We call her Alice Never On Time For Anything Miller."

Oh yes, Miller won the tournament.

She has four victories already this season and suddenly has moved to the forefront of the LPGA after seven years as a journeyman player. Miller, 29, already has broken the single season money record with $319,172 and is quite possibly the brightest new star on the tour since Nancy Lopez began practicing her artistry in 1977.

This from a player who couldn't make the golf team her senior year in college, once possessed the most atrocious swing on the tour and had a permanent hook that only can be described as mind-bending. Long one of the most well-liked players and a leader of a growing Christian movement on the tour, she also seems to be a prime example of good works paying off.

"I always thought the top players were the ones who came out as great amateurs and made it right away," Miller said. "So, I'm a strange exception. Maybe that's good, though. I've got to give some people hope."

With a rebuilt game that only came together two years ago, Miller leads the tour in virtually every statistical category. She is on top of the Mazda LPGA cumulative standings, leads the battle for points in the Rolex Player of the Year competition, is tied with Lopez and Pat Bradley for top 10 finishes with 13, has 43 subpar rounds, and leads in birdies with an average of 4.04 per round.

It is the money, however, that may turn out to be Miller's most lasting feat. The old money record was held by JoAnne Carner, who earned $310,399 in 1982. A huge increase in purses has something to do with her midseason accomplishment. In 1982 the total money on the tour was $6.7 million; now it is $9 million. But Miller has played just 18 tournaments, and two of her victories came in majors -- the McDonald's and the Nabisco Dinah Shore. It took Carner 26 tournaments, winning five of them, to set her record. With 15 tournaments remaining, Miller could double her current earnings.

Money, which used to be just something to measure her ranking by, has become a pleasure. She is the daughter of a struggling schoolteacher from the small northern California town of Marysville. She couldn't afford to go to Stanford, her father's alma mater. But now for the first time in her life, she is buying playthings -- camera equipment, a trip to Japan, a 35-foot custom-built trailer in which she travels the tour.

"It takes the pressure off financially," she said. "I never had any before. I never went hungry or anything and I had a used car in college. But I never had it to the point where I could do whatever I wanted."

Seven-year veterans do not often turn out to be bright new stars. In Miller's case, it is a question of doggedness. Despite her severe swing problems coming out of Arizona State in 1978, she decided to join the tour mainly for a lark. She did not even begin to cover her expenses until 1981.

"Even when I wasn't making any money, I didn't really mind," she said. "I always figured if it didn't work out, I could just do something else. I've always been easygoing; that's my nature. I realized as a young player it was in my best interests not to get mad. Being a club thrower was a luxury I couldn't afford."

Miller credits her gradual improvement to seven years of study under Ed Oldfield, a teaching pro at Glenview County Club in Illinois. Oldfield started by changing everything about a swing that had deteriorated rapidly at Arizona State. Her stance was unbalanced, her hands were wrong, the club face was closed and the hook had become a menace.

"I've changed everything there is to change," she said.

"She was pretty bad," Oldfield said.

Miller was a respectable junior player who made the ASU team as a freshman and had fair sophomore and junior seasons. Her swing finally caught up with her as a senior, however. She was hitting every ball into the scenery out of bounds and couldn't make the team.

"You can get away with faulty mechanics for only so long," she said. "I was having some success early, so I was reluctant to change. Maybe if I had been playing badly earlier, I would have made the changes earlier and been all right."

Oldfield is rapidly building a reputation as a brilliant swing doctor. Miller actually is his second straight success story. Last season's prodigy was Betsy King, an eight-year veteran who became the leading money winner and Player of the Year in 1984.

"He doesn't promise overnight success," Miller said. "He's not going to fix you in one lesson. But he's got the best eye I've ever seen. He sees things that I have to watch for in slow motion. The thing that really separates him is he can tell you what it should feel like."

The chief thing he requires, however, is patience. His students can expect to spend years on their swing. Miller has been with him for seven, King for five. Miller finally covered her expenses in 1981, and then began climbing the money list, finishing in the top 10 the last two seasons.

Perhaps the most exciting thing about Miller's grand entrance into the golf limelight is that she seems to be the sort who will stay there for a while. If nothing else, her journeyman quality and placid disposition may keep her there.

"Alice is going to last because she has a great ability to leave it at the course," said Judy Rankin, the leading money winner in 1976 and '77 and a golf analyst for ABC now. "She doesn't seem to have that intensity that wears you down. The bad shot or good shot isn't going to take her too high or low."

Oldfield contends Miller still has improving to do and continues to tinker with her swing, to the point that she was experimenting with it this week at the Open. It may have hurt her chances at a second major title: she had two consecutive rounds of 75 and, though she made the cut and shot 71 today, is 11 strokes off the lead.

"She's still not striking the ball the way she's capable of," Oldfield said. "So we keep grinding away, no matter what the week is. She should be better. I know that sounds strange. But she's dedicated. She has a blind faith. She's come so far now, she doesn't question anything anymore."

Miller greeted her second 75 on Friday with her usual shrug.

"Too bad," she said.