A blue-collar worker in a Seattle area Navy shipyard cannot afford a "promotion" to a white-collar job as production controller, because the move would mean an hourly pay cut from $12.20 to $10.19.

In Detroit, a man who recently joined the federal work force as an unskilled maintenance worker who mows lawns and moves furniture, makes $15,200 a year, while a beginning engineer with at least four years of college working at the same building receives only $13,600.

In a Veterans Administration hospital in Los Angeles, a newly hired janitor earns $5.42 an hour while a licensed practical nurse with 10 years of outside experience receives $5.05 an hour.

In the District of Columbia, a newly hired government typist makes $28 a week less than her counterpart at a private firm nearby, but in New Orleans, a federal typist makes $8 more than the private sector typist.

Uncle Sam's monumentally complicated system for deciding how much to pay his employes has gone haywire in a number of ways, and government officials at various agencies offer examples such as these to illustrate the impact.

The Carter administration is trying to agree on a set of changes that the president may send to Congress early next year. Officials say the changes could save billions of dollars and would reduce raises or pay levels for federal workers in a number of job categories.But they maintain the result will be a fairer distribution of the money and a more defensible system.

The current system has been attacked from several quarters, including the Chamber of Commerce, Civil Service Commission Chairman Alan K. Campbell pointed out. "If we don't get some changes made, there will be a frontal attack on the whole system and we will be forced back" to a different system that is even less in the interests of employes, he says.

Campbell and other administration officials say they realize any such proposals are likely to receive a hostile reception from members of Congress sympathetic to federal employes and their unions.The unions have expressed opposition to the changes since their recommendation several years ago.

"For a Democratic president to propose to cut the pay of working people is a sadness," said a source on the House Post Office and Civil Service Committee, which would handle the pay proposals. "The reception here would be cool and difficult, but I wouldn't say Congress wouldn't eventually adopt the changes."

The federal pay system is based on the simple principle that federal workers should be paid salaries comparable to those earned by their counterparts in the private sector.

In harsh bureaucratic reality, however, that principle tranlates into a Rube Goldberg contraption of graphs, parabolas and logarithms, of clashing "indexation and weighting methodologies," of "intergrade deviations" and "uncorrected residuals" and curve-fitting. This mathematical device spits out a questionable result that then is further punched, stretched or squeezed by politics and economics into a final pay structure.

"Some people think you look at a secretary in the private sector and she makes $4 an hour, so you give a federal secretary doing the same work $4," said Ruth O'Donnell, a Civil Service Commission pay expert, shaking her head. "Uh-uh," she said.

"One of the troubles with the federal pay system is basically that it's so damn complicated that very few people in the world actually understand it," said a National Treasury Employees Union official familiar with the process.

Union leaders contend that the complex process makes federal workers seem overpaid and that a built-in time lag keeps federal workers' pay rates several months behind those of the private sector.

The bugs in the pay system not only misspend money but also cause morale problems at federal worksites and make it difficult to recruit or hold employes in certain occupations, according to some managers.

Under the current system, for instance, blue-collar and white-collar workers are paid under two completely separate and dissimilar systems. Blue-collar pay, based on local wage rates, has risen more rapidly than white-collar pay, which is uniform nationwide.

Because blue-collar wages are based on local rates and because various special provisions give them an extra boost, federal blue-collar workers earn an average of 8 percent more than their counterparts in the private sector, officials estimated.

In several areas, such as the shipyard near Seattle, they earn more than highly trained federal white-collar workers.

"This means there is no incentive for the blue-collar guy to move into that white-collar job," a Navy official said.

Moreover, a blue-collar worker who had worked his way to white-collar status eight years ago, when it really was a promotion, cannot fall back into his old job in order to protect himself against a layoff, the official added. "Now, going back to his old job would be a promotion," the official said.

"This is a very difficult situation for us. Historically, we've gome into the blue-collar ranks for men fill these very most key-level jobs. Now where do we get trained people?" the official said.

The Defense Department, with its shipbuilding, aircraft maintenance and other industrial callings, employs more than 350,000 blue-collar workers, or more than 70 percent of the federal blue-collar work force.

Officials estimated that proposals to scale down pay rates gradually in the blue-collar system eventually could save $500 million a year in workers' paychecks, if Congress approves the move.

The Defense Department would save more than $1.9 billion between now and 1983 on blue-collar wage costs, if the changes are adopted, officials said.

Traditional pay relationships have been upset "because of the wackiness of the system and not because of any logical evaluation of what the work is worth," said Frederick A. Kistler of the Bureau of Policies and Standards at the Civil Service Commission.

For years, commissions and independent observers have been recommending changes in the federal pay system. The Carter team planned to include such recommendations in its civil service reform proposal that became law last fall after a tough battle in Congress. The planners decided to postpone the pay package because it was one controversy too many for the already complex plan.

In addition to the phased reduction in blue-collar pay, the Carter team also is considering:

Splitting clerical and technical workers from professionals such as chemists and accountants and paying them according to local rates instead of one uniform nationwide rate.

The current system places them together in a given level and pays them equally. So secretaries tend to be overpaid, while junior professionals are underpaid compared with their peers in the private sector, officials said. The situation was worse until certain reforms of the pay formula were initiated in 1976, they added.

Also, workers in high-cost areas such as New York City are "wildly underpaid" while federal employes in low-pay areas such as Dothan, Ala., are the local "fat cats," officials said.

About 400,000 employes are overpaid and 300,000 are underpaid in this context, one Civil Service Commission expert estimated.

Including in the pay formula retirement, vacation and other fringe benefits the government provides its employes. The process currently ignores these items.

Some experts said that, because government benefits are so generous compared with those of the private sector, this new way of calculating pay would mean lower annual pay raises for virtually all white-collar workers.

There is disagreement within the administration in this area, officials said, about such questions as how to measure benefits. For example, should job security and easier promotions be included? And some said that because no valid comparison of private and federal benefits has been made, the effect the new calculation would have on workers' pay cannot be predicted.