The chairman of the Federal Reserve Board, the nation's central bank, has often been called the second most powerful man in Washington.

In recent months, however, some of that power has been questioned as G. William Miller, President Carter's hand-picked successor to Arthur Burns, settles into the job some of that power has been questioned.

Although the chairman of the independent Fed receives most of the public attention, the fact remains that he has one vote out of seven on the Federal Reserve board of governors and one out of 12 on the monetary-policy-making Open Market Committee.

No Federal Reserve chairman can be outvoted consistently and remain effective (and Miller during his four-month tensure, Burns, and Burns' predecessor, William McChesney Martin, have not been), but the importance of the other governors and the five nongovernors on the Open Market Committee increases during a chairman's "neophyte" period - as he learns the ropes, the personalities and how to bring the board around to his way of thinking.

Miller himself has observed that his fellow governors casually ignore the the "thank you for not smoking" signs that Miller, a nonsmoking former Textron Corp. chief executive, put up in the Fed's boardroom. In a recent vote on whether to raise the discount rate the central bank charges its members to borrow from it, Miller was on the losing end of a three-to-two tally. He had urged his fellow governors to hold off.

But much to the chagrin of many of his liberal supporters who thought he would lean against the wind at the inflation-conscious Federal Reserve Miller's anti-inflation rhetoric, as well as most of his votes in the Open Market Committee, sound and look curiously like those of his fellow governors as well as of his predeccsor.

That should surprise no one.

As one top administration policy maker observed, the Fed's role has been that of inflation-fighter for so long that no chairman could or would want to change. Furthermore, a chairman who was in violent disagreement with his fellow governors soon would find himself ineffectual, another observer noted.

"The point is, Miller is not a captive of his institution any more than Burns or Martin was," ont top congressional obserrver said. "If you listen to him - and there's no reason to think he doesn't believe what he says - Miller approaches inflation and monetary policy in much the same way as his fellow governors."

Miller himself has said that his vote against the discount rate increase was a cautionary one because he wanted to wait to see more evidence on money supply growth. If he had to vote today, he would vote with the majority, he said in a recent interview with The Washington Post.

The Federal Reserve is an independent agency whose day-to-day decisions on monetary policy are subject neither to presidential nor congressional challenge, although the central bank reports to Congress every three months to discuss its goals and plans.

But both its independence and its power are more technical thatn real. The Fed, insulated as it is from day-to-day political pressures (governors serve 14-year terms), can take much sterner anti-inflation actions than can a president or a Congress. The Fed, however, cannot long thwart congressional or administration intent and maintain its independence.

And studies by economists such as Robert Weintraub, staff director of the House subcommittee on domestic monetary policy, demonstrate that the nation's money managers know this and seldom pursue a course of action that is at variance with what the administration and Congress desire.

Miller was sworn in as chairman of the Fed on March 9. Burns resigned on March 31, and the administration soon will nominate Nancy Teeters, chief economist of the House Budget Committee, to fill out the remainder of Burns' term. Teeters is thought of as a liberal economist who probably will be more reluctant to use high interest rates to fight inflation than most of her colleagues.

The other members of the Boards of Governors, all of whom sit on the Open Market Committee as well, are:

Henry Wallich, a German-born Yale economist, who many consider the best economic mind on the board. Wallich probably shares the board's general concern about inflation, but has been in the forefront of economists looking for ways to fight inflation through direct influence on wage and price behavior (so-called incomes policies) in order to take some of the pressure off monetary and fiscal policies in fighting inflation.

J. Charles Partee, a former top Federal Reserve staffer. Partee is also a well-respected economist - he was director of research at the Fed - who fights hard for his position in Fed board meetings. Partee is a little less agressive on inflation thatn most governors, according to board sources. He was the only governor to vote with Miller against raising the discount rate last month.

Philip Coldwell, an economist and former president of the Dallas Federal Reserve Bank. Coldwell has spent most of his life in the Federal Reserve system.

Philip Jackson, a noneconomist who was a mortagage banker before he was named to the Fed board. Jackson tends to vote in the majority on major monetary policy decisions.

Stephen Gardner, who was deputy secretary of the Treasury in the Ford administration. Gardner is vice chairman of the board, but has been ill in recent weeks. He too has tended to vote with the majority in major policy decisions.

Besides the sitting governors, five of the 12 Federal Reserve district bank presidents sit on the Open Market Committee, who meets monthly to decide the course of monetary policy:

Paul Volcker, president of the New York bank and a permanent member of the Open Market Committee. Volcker, a Democrat, was Treasury under-secretary during the difficult international monetary negotiations in President Nixon's first term. The tall, gruff former Chase Mahattan banker is the most important of the district bank presidents. The New York Fed operates the trading desk that carries out the directives of the Open Market Committee.

David Eastburn, president of the Philadelphia bank. Eastburn is an economist who tends to vote with the majority on most monetary policy decisions.

Willis Winn, president of the Cleveland bank. Winn was one of two members of the Open Market Committee who voted in June against tightening the money supply slightly. Winn wanted the Fed to take more aggressive action against the expanding money supply.

Ernest Baughman, president of the Dallas bank. A former top staffer at the Chicago branch, Baughman has tended to vote with the majority.

Mark Willes, president of the Minneapolis Federal Reserve bank, Willes, who brings some monetarist leanings to the Open Market Committee, also wanted the central bank to take stronger action against inflation and the growing money supply at the June meeting.