The Army will try again Friday to launch a successful flight test of its Pershing II missile, according to Undersecretary of the Army James R. Ambrose, who said yesterday that he expects this one to work.

After two test failures and a postponement last Friday, Ambrose went Tuesday to the Florida plant of Martin Marietta Co., the missile's prime contracter, for a full-scale review of the troubled program.

He said in an interview yesterday that development of the missile, a key to modernizing the North Atlantic Treaty Organization's medium-range nuclear weapons in Europe, was "still on schedule."

"We see nothing in prospect," he said, "that will cause enough change" to delay planned deployment of "a small number" of Pershing II missiles in West Germany in December, 1983.

But he added that the missile program was "up against a crack" and its problems could become cumulative. "If the thing is known in Europe to be not working, then you have got a bigger political problem" deploying rather than delaying it, Ambrose said.

The Army originally had not expected to deploy the Pershing II until December, 1984, but a hurry-up schedule was established to meet a NATO-approved deadline for deployment.

From bases in West Germany, the Pershing II could hit targets inside the Soviet Union within eight minutes. Since NATO agreed in December, 1979, to deploy 108 Pershing IIs, the missile has been the target of European peace movements and Soviet propaganda.

The missile also is a factor in U.S.-Soviet negotiations in Geneva on mutual reduction of nuclear arms in Europe.

To meet the NATO deadline, the Pershing II is technically already in production although the missile has not yet undergone a successful flight test.

When first tested last July at Cape Canaveral, the missile exploded 17 seconds after launch.

Ambrose said yesterday that a new first-stage motor had to be built and several of those "already built had to be rebuilt."

He said technicians have not been able to determine what happened in the second test, when onboard batteries failed to turn on properly to provide electrical power for the missile in flight.

Last week's postponement, he said, was due to discovery of bad electrical components in the guidance system. All 170 of them have now been changed.

Friday's test will be at White Sands, N.M., where the two-stage missile is to be launched 200 miles almost straight up and 100 miles downrange.

This test is designed primarily to see how the new terminal guidance system works. It also will test the rocket's engine.

A second White Sands test is scheduled for December before the Army returns to Cape Canaveral for two more shots at the missile's full range of up to 1,000 miles.

Ambrose said yesterday it would take eight or nine tests before the missile could be seen operating under "all the extremes."

The undersecretary said that "by the time you fire 10 to 12 successful test shots" you can be confident the missile works.

On Tuesday, a House Appro- priations subcommittee cut $504 million in production funds from the fiscal 1983 defense money bill.

Members said the money would be held up until the Pershing II successfully completed its testing program.

Ambrose said yesterday, however, that already-approved fiscal 1982 production funds were available to pay for the first few Pershings.