The Fairfax County Board of Supervisors, faced with statistics showing that about one in seven county residents has an alcohol abuse problem, endorsed a comprehensive alcohol treatment program yesterday.

The program , expected to begin next summer, was descriped as the county's most ambitious effort to deal with its alcohol abuses, including an estimated 19,000 alcoholics. It would increase out-patient services for persons with alcohol problems and pool existing services under a central director while easing the caseload for hospitals and other in-patient facilities.

The proposal was developed and presented to the supervisors by the Fairfax Hospital Association and the Fairfax-Falls Church Community Services Board. Michael Green, assistant director of planning for the community services board, said the treatment program should not cost the county much more than the $1.4 million it now spends on alcohol abuse services.

The Washington area has one of the highest incidences of alcohol abuse in the nation, according to specialists in the field. Nationally, one in 10 persons has a drinking problem serious enough to cause the loss of a job, marital trouble or arrest.

"Our present treatment facilities are overpopulated," said John M. Hardy, director of alcohol and drug programs for the community services board. "We have people we are turning away or people we are not able to help on a timely basis."

Hardy and other treatment care experts told board members that the concept of out-patient facilities for alcohol abusers is relatively new in the nation but has shown good results. It also has been less expensive to operate.

"We hope to reach more people and bring them into a treatment program," Hardy said. Detoxification and rehabilitation efforts, he added, work better on an out-patient basis when the family as well as the one with the drinking problem is involved.

The county's three hospitals handle about 10 to 12 patients a day in their treatment units, but the rate of recidivism is reported to exceed 50 percent.

After expressing surprise at the county's alcohol abuse statistics, board of supervisors members queried treatment experts about the program's impact on jailed prisoners who have drinking problems.

Sheriff James Swinson told the board he expected the revamped system "to help take some pressure off the jail." But he cautioned that problem drinkers charged with felonies would need special security arrangements that do not now exist at the county hospitals.

"This program sounds excellent, but I've heard this song before," Swinson said. He reminded the board that he had unsuccessfully urged them to include secure hospital facilities for jail inmates when a new wing was added to Fairfax Hospital in 1967.

Hardy noted that the county already is providing counseling services for jail inmates with drinking problems, and he said that the new proposal would provide follow-up services once they are released.

But, Hardy emphasized, "the majority of the people we treat don't come to us through the criminal justice system."

Operators of the program are applying for a U.S. grant to help defray some of the costs and expect to recoup much of their expenses through reimbursement from private insurance companies that have been increasingly willing to provide coverage for out-patient treatment.