HOW IS IT, people ask, that so experienced and successful a playwright as Arthur Miller can come up with a play greeted so negatively as his new work, "The Archbishop's Ceiling," at the Eisenhower?

The play begins with the visit of an American writer to an admired colleague who is alienated from the government of his Iron Curtain country. Associates of lesser stature have greater freedom, and a link between all the characters is a beautiful woman who is both writer and actress. Does the dissident plan to leave his homeland?

Neither the play's reception nor the situation is as simple as it seems. Every new play, however august the auspices, is as experimental as the most avant-garde piece born in a walk-up attic or a cellar. Computers don't write plays.

While the notices so far have been poor, there are those who see God as a symbol in the powerful voice directing Miller's characters. Others find it the best talk they've heard in a theater in too long. Certainly, audiences are listening, a sign that there is life at the play's core.

Though Miller has spent 2 1/2 years on the play, just getting it written and onto a stage is anything but simple. In truth, the play's production and reception reflect in microcosm our theater's present combination of economics, work rules and changing conditions.

"The Archibishop's Ceiling" was not intended to continue beyond the Eisenhower's closing date, May 28. The engagement was planned as a shakedown before a New York production next fall to get the feel of the play, its problems and weaknesses. Years ago, this was a common approach for starting a new play. Newark and Atlantic City used to see just such short test runs.

No one connected with "The Archbishop's Ceiling" seems satisfied with it but, most of all, producer Robert Whitehead blames himself.

Lean, gentlemanly Whitehead, a longtime partner of Kennedy Center chairman Roger L. Stevens when Stevens is wearing his New York hat, is the cream of American producers. Besides Miller's previous plays, "The Price" nd "The Creation of the World and Other Business," Whitehead's offerings lately have including "A Texas Trillogy," Katharine Hepburn's " A Matter of Gravity," which last night ended its long tour in Baltimore, as well as such memorable ones as "The Visit," "The Member of the Wedding" and "A Man for All Seasons."

So experience and judgment went into the production. But theater reflects life in that conditions always are changing.

Once the wheels are set in motion, choices narrow. Initially, the play was to have been introduced by New Haven's Long Wharf Theater, one of America's most respected regional theaters. Then it developed that Miller's script would not be ready for January rehearsals. Long Wharf's director, Arvin Brown, filled the announced Miller slot with another offering for his subscribers. Later a hole developed in the Eisenhower's May schedule. Stevens suggested that perhaps the Miller play could test its values then. Whitehead asked Miller, Miller said he could be ready and Whitehead assigned the direction to Brown, familiar with the play and whose Long Wharf works have been transferred successfully to Broadway.

Now the time clock started ticking.Whitehead assigned set design to David Jenkins, whose work has included assignments for Arena State ("One Flew Over the Cuckoo's Nest," "Boccaccio" and "Relatively Speaking") as well as Long Whart and Broadway, Jenksins determined on using the sitting room, where most of the action takes places, as the focal point of his design, using spaces to both sides of the stags for scenes elsewhere. This would work in some theaters, but the Eisenhower's spaces are not so adaptable.

All the play's major characters except for the one American are citizens of an Iron Curtain country. Here casting choices come into play. Equity regulations make employment of non-Americans difficult; only unique "star" players are exceptions to the rule. Because she had an Equity card in force from an earlier contract, Bibi Anderson was available for the central famale role. A clue of uncertainty was revealed in the replacement of Gig Young with Douglass Watson, since they are wholly dissimilar actors. Five days before rehearsals were to begin, Brown received Miller's completed script.

By now the timetable began flashing in neon. Getting the play ready to open on schedule became priority Numero Uno. By then, Whitehead was aware that basic choices, by now unalterable, were not going in the direction planned. Opening night was put off until Saturday, to enable the cast to have three preview performances before its official first night.

None involved felt that was a satisfactory opening and to these experienced professionals unfavorable notices were no surprise.

As a member since her teens of Sweden's Royal Dramatic Theater and, from her American stage bow several years ago in Erich Maria Remarque's "Full Circle," Bibi Andersson already had been a victim of our production madness, but hoped for better luck this time. Later she mused how her state theater at home handles a new script:

"We would read it anc rehearse it for months - six, even eight. If the casting wasn't right, roles would be switched, given to other members of the company. Then would come full rehearsals with scenery and props and lighting. If it still wasn't right, the production would not open until further work was done. Only when it was absolutely ready, with no time clock for theater rentals, subscription lists, actors' availability, involved.Nor would a play be presented officially to the critics after only three performances. It takes playing for characterizations to jell, something beyond getting the lights on cue."

This is the difference between the subsidized theaters of some European countries and the timetable that has governed new American productions for several generations.

Under the evolving maturity of our American regional theater, this system is changing, but traditionally experienced hands still hew to it. Further, existing theaters need attractions. Any producers or manager would welcome introducing a Miller work. Whitehead was cautious enough to budget his Eisenhower production close to a break-even point. Actors, who get only a fraction of their salaries for the rehearsal period, are proud to create Miller characters and, if need be, will take less than they get from TV or films.

Because its productions are expected to pay their way from the start, the Kennedy Center prefers its productions to open as soon as possible, so word will get around and cash will flow into the box office. In stores if shoes don't sell the first day, they many later. In theaters an empty seat is a nonsale for all time. This experience and others suggest two solutions: pre-center engagements or a longer series of previews but at reduced prices.

For these multitude of reasons, the first version of "The Archbishop's Ceiling" will end on the 28th.

How does Miller react to this?

"Of course I'm disappointed but I'm far from giving up on the play. There's something there in this story, these characters, which the audiences are listening to. Already some staging changes have improved things in the first act. I'll be getting to work on the changes in a few weeks.

"I think of the play as string quartet, yet not unlike 'The Price,' which also had four voices. They must be exact in writing and sound and casting. The Equity regulations, keeping European actors from European roles here, are a sorry problem. And the Eisenhower seems like such a big theater though it isn't, with 1,104 seats. The focus on its stage is constricted by distance. You know, audiences do not listen to speakers they cannot which speaking. It's curious but a fact.

"Your man who saw God in the play is quite right, though I certainly didn't know it while working on it. Actually there are three complete versions of this play, all bound and ready to go. On one of them I must have completed 24 drafts.

"I think of the play as a widening, lateral movement of how we all are affected by things, powers, beyond us, circumstances and people of which we have not only no control but no knowledge. These people all are affected by this vague, distant power. I'm not condemning Marcus, the regime's favored writer. I'm trying to explain his condition and unseen controls.

"Your friend who mentioned the play as being about God, moves me to think of Sigmund, the dissident writer, as Christ. He knows that the time will come when he must openly, actively oppose Marcus.

"The second act begins when Maya (the Bibi Andersen role), whom you might think of as Magdalene, knows Sigmund has retreated to the bedroom, needing to be alone to gather this forces, his nerves. This is the time when Sigmund must have his apartness in a desert, a garden or, in this case, the bedroom, a quiet time."

Miller understands this need for his writing. "That's why I've chosen to live all these years on a Connecticut farm 100 miles from New York. It's not a place where people just drop in casually. And people do think twice about spending 80 cents on a phone call from the city.

"I'm an early riser, at may desk by 6:30 and work throughout three or four days at a stretch. My wife (photographer Inge Morath) and I have just published our second collaboration, 'In the Country' Besides the plays I'm always working on, I'm also writing a book, well, maybe it will be a novel, but it won't be ready for some years yet, very much about our times.

"I've also had a good deal of pleasure working on the musical version of "The Creation of the World and Other Business,' which didn't work too weel either here at the Eisehower. Since then Stanley Silverman has composed a score for a new version we did at the University of Michigan. My, I enjoyed that, no pressures. Even wrote and put in two new songs during the week it played. Now we have been tightening it with more material and when Stuart Ostrow heard about it, he asked if we'd like it done in his new Musical Theater Lab on the Kennedy Center roof. That's what I've been getting ready these past few days. It goes into rehearsal on the 14th and will be performed, free, you know, for two weeks starting June 14.

"Something very satisfying about that," Miller laughed."The critics don't review Musical Theater Lab productions and we don't need to sell seats. Just work on it with no pressures."