An armed 19-year-old man with a history of family violence was fatally shot by Fairfax County police early yesterday six hours after he barricaded himself inside his parents' home in the affluent, normally quiet Mount Vernon area.

Robert Staudaher emerged from a second-floor bedroom firing a .30-caliber carbine after police used tear gas to try to end the siege, police said. Staudaher was hit in the abdomen by a single return shot by Sgt. Daniel Grimes and was pronounced dead shortly after 4 a.m. at Mount Vernon Hospital.

Staudaher's mother, Martha, and sister locked themselves in a bedroom and later were released unharmed after police used a bullhorn to negotiate their release. His father, Fred, escaped down a fire ladder from a second-floor window.

About 20 neighbors were evacuated from the street of $150,000 colonial-style houses and waited out the incident at nearby Mount Vernon Hospital.

Police, who said the incident began as a family quarrel and escalated into an assault by Staudaher on his mother, said the teen-ager had access to several handguns and rifles kept in the house at 7401 Range Rd.

They said that in the midst of the siege, the young man's mother initiated a legal proceeding with a Fairfax County magistrate to have her son taken into custody on mental grounds, but that police were unable to serve the petition.

Staudaher had been involved in at least two similar incidents in the past, according to authorities. Last year he was served with two separate warrants in connection with alleged assaults on his mother. Records of the cases are held by the county's juvenile court and are private.

Staudaher family members refused to discuss the episode yesterday, and most residents of the neighborhood of clipped lawns, basketball hoops and children's bicycles were equally reticent.

"They're my neighbors and I have to live here," said one man as he scraped paint from a second-floor balcony.

"The first three months we were here we had to accustom ourselves to the quiet of the street," said a woman three doors away. "People here are all absorbed in their own lives and in keeping their front lawns nice."

Some, who said they had been up all night waiting at Mount Vernon Hospital, answered their doors yesterday afternoon in night clothes and with bloodshot eyes. "I just feel so sorry for them," said one.

Others said they had heard the Staudahers remark earlier that they were looking for counseling for their son, that Robert Staudaher had an attitude problem" and "didn't want to work."

Staudaher, a former varsity football player, had dropped out of Groveton High School in February 1979, his senior year. The school's principal, R. Donald Ford, said Staudaher was an "excellent student" in auto mechanics.

Staudaher "wasn't making much progress in other subjects," Ford said, and quit school with a record of absenteeism.

Still, Ford said Staudaher was never a discipline problem. "We hardly recognized his name when we heard the news," Ford said.

"The people I talked to were very surprised, as I was," Ford said. "He was basically a loner. He didn't have very many friends. But he didn't seem to be the kind of kid who would end up like this."