Virginia has cited Dan River Inc., the state's second largest private employer, for failing to meet a federal deadline for installing equipment to meet cotton dust standards at their textile mills. The state did not fine Dan River, however, saying that the company was moving as quickly as possible to install the equipment.

The company, which employs 8,000 workers, received a technical "citation without penalty," according to a letter sent to Dan River from Virginia Labor Commissioner Eva S. Tieg. The citation, dated Nov. 5, requires the firm to submit progress reports to the state every 90 days.

The federal government imposed a March 27, 1984, deadline for the installation of expensive ventilation equipment to reduce much of the airborne cotton dust in Dan River's mills.

Byssinosis, brown lung disease, a sometimes fatal pulmonary disorder found among textile workers, is commonly thought to be caused by airborne cotton dust that is small enough to enter the lungs.

Several months before the deadline, Dan River asked the state, which is responsible for implementation of the worker protection rules, to exempt it from the regulations, which could cost the company more than $7 million. Dan River had already spent $24 million to lower cotton dust levels in many areas of the Danville plant, but 10 percent of the plant still failed to meet the new federal standards.

Dan River told Virginia officials it wanted to study the cause of brown lung disease by exposing workers to more cotton dust than the new federal rules allow. Virginia granted the textile company a six-month extension and said it would consider a permanent one after evaluating data submitted by the company.

The action prompted heated protests from members of Congress and labor groups, who said it was tantamount to "human experimentation." In July, Dan River withdrew its request for a variance because of the negative publicity, and it promised to install the ventilation equipment.

"Our compliance program is proceeding on schedule," Dan River spokesman Jane Pritchard said yesterday. According to a plan submitted to the state by Dan River, the entire plant will meet federal standards for cotton dust by Oct. 4, 1985.

In her letter to Dan River, Tieg wrote that the company's plans are "appropriate and expeditious." But she said because the plans will take a year to implement, and because the request for a variance has been withdrawn, the company is technically out of compliance with state and federal cotton dust laws.