The Fairfax Hospital Association, in a bid to improve relations with some of its critics, has begun to take the wraps off its finances. In the process, the agency has announced it will increase room rates at its Northern Virginia hospitals by 9.5 percent.

Release of what the association calls the most detailed budget it has ever disclosed has left some members of the county board of supervisors -- who have complained that the independent association operates with too much secrecy -- unimpressed.

"It's come part of the way, but it still has not gone far enough," said Supervisor Audrey Moore, who is a member of the association's 30-member board of trustees as well. "The budget is still impossible to read for anyone who isn't working with it on a day-to-day basis."

The nonprofit association released the 183-page financial plan just days before it girds to battle Humana, Inc. -- the nation's second largest for-profit hospital chain. Humana this month plans to seek permission to build a $34 million 200-bed hospital in Reston.

The association has allocated $1 million in the budget to plan for possible replacement of its Fairfax City hospital to a site near the Humana hospital. County supervisors and association officials agree the association report contains detailed information on employe wage increases, capital expenditures and cost figures for the association's three hospitals, although some officials said it was not enough.

"It's really wrong to expend public funds without a full accounting, no matter how small the expenditure is," said Supervisor Martha V. Pennino. "No one is criticizing the quality of medical care patients receive. But we want to be assured that the medical costs to patients are accurately reflected in their bills."

The association's top official disagreed that the budget details were insufficient. "I believe we've gone as far this year as we know how to go in terms of meeting what they are asking for," said Franklin P. Iams, president of the association. "Each year we've made changes in our budget format so it will assist them in reviewing it. It the budget is more detailed than anything we've done so far." He said the plan will go to supervisors for comment before association trustees vote on it Dec. 22.

For years, supervisors have feuded with the association over whether supervisors can exercise any oversight over the health-care facilities the county helps fund. Some supervisors argue that the county government should be more involved in hospital operations since Fairfax taxpayers pay the $3 million a year in debt on bonds used to build the 150-bed Mount Vernon Hospital, off Rte. 1, as well as the Access emergency care unit in Reston. The association also operates the 646-bed Fairfax Hospital on Gallows Road and the 135-bed Commonwealth Doctors Hospital in Fairfax City.

The $151.5 million 1982 budget would boost patient costs about $27.80 per day, from $292.20 currently to a projected $320. The fiscal plan also calls for $14.7 million in new equipment purchases and capital expenditures, including $1 million in new radiology equipment and $500,000 for a new telephone switching and paging system at Fairfax Hospital.

Semiprivate room rates at the association's hospitals would go from $142 to $155 a day. Although there are no figures to compare association patient care costs with other hospitals, a July 1981 survey by Blue Shield showed that the association's three hospitals were about $38 cheaper than the $179 area-wide average daily rate for a semi-private room.

Association officials attributed the increases to inflation and higher costs for food, medicine and utilities. But a large chunk of the increase is tied to association workers who will receive a 10 percent wage boost totaling $7.1 million. The association also plans to spend another $3 million to hire 203 workers.