The Fairfax County Board of Supervisors, responding to the shortage of day care centers in Northern Virginia, is trying to encourage corporations to open facilities to take care of children during work hours.

Twice in the past month, Fairfax politicians have proposed that the county take steps to make day care centers in office and industrial parks viable and to urge small companies to form day care associations.

The county board has asked its staff to examine how state and local regulations might be changed to ease the way for firms thinking of opening day care facilities.

Board Vice Chairwoman Martha V. Pennino has proposed changing a county ordinance that hinders firms from opening day care facilities on their premises.

Board Chairman John F. Herrity asked the county staff to study what incentives might be offered to firms in order to encourage the centers.

Herrity and Pennino said that one obstacle to promoting the centers is exacting state regulations; they added that some regulations could be modified without compromising day care quality. Herrity stressed that the county would continue to scrutinize the backgrounds of employes in the centers.

In other action Monday, the board reiterated its desire to reverse current county policies that allow developers to contract directly with private engineers for inspections of building foundations.

County statistics show that county inspectors are far more likely to find faults with foundation work than are private engineers who are paid directly by developers, said Claude G. Cooper, director of the county's Office of Environmental Management.

County inspectors, who look at basement footings, walls, floors and the soil alongside exterior walls, rejected 17.1 percent of the projects they viewed during fiscal year 1985, which ended last June. Private inspectors working for developers rejected just 0.1 percent of the projects during that time, according to the statistics.

Cooper said the practice of private engineers working directly for developers will end within two months.

He said private engineers could still perform foundation inspections on contract with the county.

"If the county pays," said Cooper, "they're likely to be more fair and impartial."

The county first permitted private firms to perform inspections of foundations for developers in 1978. That shift was prompted by the heavy workloads faced by county inspectors.